Question 1

Determine an equation that may represented by the graph shown below.

A) $f ( x ) = | x + 1 | - 1$
B) $f ( x ) = | x - 1 | + 1$
C) $f ( x ) = | x + 1 | + 1$
D) $f ( x ) = | x - 1 | - 1$
E) $\quad f ( x ) = - | x - 1 | + 1$

Accepted Answer

C

Question 2

The scatter plots of different data are shown below. Determine whether there is a positive correlation, negative correlation, or no discernible correlation between the variables.

A) positive correlation
B) negative correlation
C) no discernible correlation

Accepted Answer

A

Question 3

Hooke's Law states that the force $F$ required to compress or stretch a spring (within its elastic limits) is proportional to the distance $d$ that the spring is compressed or stretched from its original length. That is, $F = k d$, where $k$ is the measure of the stiffness of the spring and is called the spring constant. The table below shows the elongation $d$ in centimeters of a spring when a force of $F$ kilograms is applied.
$\begin{array}{|c|c|}
\hline \text { Force, } \boldsymbol{F} & \text { Elongation, } \boldsymbol{d} \
\hline 20 & 3.5 \
\hline 40 & 6.3 \
\hline 60 & 10.0 \
\hline 80 & 13.3 \
\hline 100 & 16.5 \
\hline
\end{array}$

Find the equation of the line that seems to best fit the data.
A) $\quad F = 12.098 d$
B) $F = 3.024 d$
C) $\quad F = 6.049 d$
D) $\quad F = 4.537 d$
E) $\quad F = 7.561 d$

Accepted Answer

To find the spring constant $k$, we can use the formula $F = k d$. By calculating $k$ for each pair of $F$ and $d$ values and averaging them, we find that the best fit is approximately $k = 6.049$. Thus, the equation is $F = 6.049 d$.

Question 4

Which equation does not represent $y$ as a function of $x$ ?
A) $x = 2 y + 5$
B) $\quad x = 6$
C) $y = - 5 x - 7$
D) $y = \left| 6 + 9 x ^ { 2 } \right|$
E) $y = \sqrt { - 8 + 4 x }$

Accepted Answer

The answer of Which equation does not represent $y$ as...

Question 5

Find the slope-intercept form of the line passing through the points.
$( - 1 , - 6 ) , ( 0 , - 2 )$
A) $y = 4 x + 23$
B) $y = 4 x - 2$
C) $y = \frac { 1 } { 4 } x - \frac { 23 } { 4 }$
D) $y = - \frac { 1 } { 4 } x + \frac { 1 } { 2 }$
E) $y = - 4 x - 10$

Accepted Answer

The slope $m$ is calculated as $\frac{-2 - (-6)}{0 - (-1)} = \frac{4}{1} = 4$. Using the point-slope form $y - y_1 = m(x - x_1)$ with point $(0, -2)$, we get $y = 4x - 2$.

Question 6

Determine the domain and range of the inverse function $f ^ { - 1 }$ of the following function $f$.
$f ( x ) = - | x + 6 | + 2$, where $x > - 6$
A) Domain: $[ - 6 , \infty )$; Range: $[ 2 , \infty )$
B) Domain: $( - \infty , 2 ]$; Range: $[ - 6 , \infty )$
C) Domain: $[ - 6,2 ]$; Range: $[ - 6 , \infty )$
D) Domain: $( - \infty , - 6 ]$; Range: $[ - 2 , \infty )$
E) Domain: $( - \infty , \infty )$; Range: $( - \infty , \infty )$

Accepted Answer

The domain of $f^{-1}$ is the range of $f$, and the range of $f^{-1}$ is the domain of $f$. For $f(x) = -|x+6| + 2$, the output decreases as $x$ increases, starting from $2$ when $x > -6$, thus the range of $f$ is $(-\infty, 2]$, making it the domain of $f^{-1}$. The original domain of $f$ is $(-6, \infty)$, which becomes the range of $f^{-1}$.

Question 7

Use function notation to write $g$ in terms of $f ( x ) = x ^ { 3 }$.
$$g ( x ) = - \frac { 1 } { 5 } ( x + 4 ) ^ { 3 }$$
A) $\quad g ( x ) = - \frac { 1 } { 5 } [ f ( x ) ] ^ { 3 } + 4$
B) $g ( x ) = - \frac { 1 } { 5 } [ f ( x ) + 4 ]$
C) $g ( x ) = - [ f ( x ) ] ^ { 3 } + \frac { 64 } { 5 }$
D) $g ( x ) = - \frac { 1 } { 5 } [ f ( x ) ] ^ { 3 } + 64$
E) $\quad g ( x ) = - \frac { 1 } { 5 } [ f ( x + 4 ) ]$

Accepted Answer

Given $f(x) = x^3$, to express $g(x) = -\frac{1}{5}(x + 4)^3$ in terms of $f$, we substitute $x + 4$ for $x$ in $f(x)$, resulting in $g(x) = -\frac{1}{5}f(x + 4)$.

Question 8

Find the difference quotient and simplify your answer.
$f ( w ) = - 9 w ^ { 2 } + 2 w , \quad \frac { f ( 4 + h ) - f ( 4 ) } { h } , h \neq 0$
A) $10 + h$
B) $- 70 - 9 w + \frac { 16 } { w }$
C) $2 - 9 w + \frac { 16 } { w }$
D) $2 - 9 h$
E) $- 70 - 9 h$

Accepted Answer

The difference quotient for the function $f(w) = -9w^2 + 2w$ is calculated by substituting $w = 4 + h$ and $w = 4$ into the function, then finding the difference and dividing by $h$. Simplifying the expression $\frac{-9(4+h)^2 + 2(4+h) + 9(4)^2 - 2(4)}{h}$ results in $-70 - 9h$.

Question 9

Determine the domain of $g ( x ) = \frac { 1 } { x ^ { 2 } - 49 }$.
A) $[ - 7,7 ]$
B) $( - 7,0 ] \cup [ 0,7 )$
C) $( - \infty , - 7 ) \cup ( - 7,7 ) \cup ( 7 , \infty )$
D) $( - \infty , - 7 ] \cup [ 7 , \infty )$
E) $( - \infty , \infty )$

Accepted Answer

The function $g(x) = \frac{1}{x^2 - 49}$ is undefined when the denominator is zero, which occurs at $x^2 - 49 = 0$, or $x^2 = 49$. Solving for $x$, we get $x = \pm7$. Therefore, the domain excludes $-7$ and $7$, making the correct domain $(-\infty, -7) \cup (-7, 7) \cup (7, \infty)$.

Question 10

If $f$ is an even function, determine if $g$ is even, odd, or neither. $g ( x ) = - f ( x - 2 )$
A) even
B) odd
C) cannot be determined
D) neither

Accepted Answer

The answer of If $f$ is an even function, determine...

Question 11

Evaluate the function at the specified value of the independent variable and simplify.
$\begin{array} { l } 
q ( p ) = \frac { - 2 p } { 5 p - 2 } \
q ( x - 9 )
\end{array}$
A) $\frac { - 2 x + 18 } { 5 x - 47 }$
B) $\frac { - 2 x - 18 } { 5 x - 47 }$
C) $\frac { - 2 p + 18 } { 5 p - 47 }$
D) $\frac { 18 } { 43 }$
E) $- \frac { 18 } { 47 }$

Accepted Answer

To find $q(x - 9)$, substitute $x - 9$ for $p$ in the given function $q(p) = \frac{-2p}{5p - 2}$. This results in $q(x - 9) = \frac{-2(x - 9)}{5(x - 9) - 2}$, which simplifies to $\frac{-2x + 18}{5x - 45 - 2} = \frac{-2x + 18}{5x - 47}$.

Question 12

Compare the graph of the following function with the graph of $f ( x ) = | x |$.
$y = \left| \frac { 4 } { 9 } x \right|$
A) vertical shift of $\frac { 4 } { 9 }$ units up
B) horizontal stretch of $\frac { 9 } { 4 }$ units
C) vertical shrink of $\frac { 4 } { 9 }$ units
D) horizontal shrink of $\frac { 4 } { 9 }$ units vertical shift of $\frac { 9 } { 4 }$ units
E) horizontal shrink of $\frac { 4 } { 9 }$ units

Accepted Answer

The function $y = \left| \frac { 4 } { 9 } x \right|$ represents a horizontal stretch of the graph of $f(x) = |x|$ by a factor of $\frac { 9 } { 4 }$, because the coefficient $\frac { 4 } { 9 }$ inside the absolute value affects the x-values, making them $\frac { 9 } { 4 }$ times wider to achieve the same y-values as the original function.

Question 13

Use the graph of $f ( x ) = x ^ { 2 }$
to write an equation for the function whose graph is shown.

A) $f ( x ) = ( x + 1 ) ^ { 2 } - 2$
B) $f ( x ) = ( x - 1 ) ^ { 2 } - 2$
C) $f ( x ) = ( x + 1 ) ^ { 2 } + 2$
D) $f ( x ) = \frac { 1 } { 2 } ( x - 1 ) ^ { 2 } - 2$
E) $f ( x ) = \frac { 1 } { 2 } ( x + 1 ) ^ { 2 } - 2$

Accepted Answer

The answer of Use the graph of \(f ( x...

Question 14

Determine algebraically whether the following function is one-to-one $| x - 5 | , \quad x \leq 5$
A)
$\begin{aligned}
| a - 5 | & = | b - 5 | \
5 - a & = 5 - b \quad ; \text { one-to-one } \
- a & = - b \quad \
a & = b
\end{aligned}$
B)
$\begin{aligned}
a & = b \
| a - 5 | & = | b - 5 | \
| a | - 5 & = | b | - 5 \
| a | & = | b | \quad \text { one-to-one } \
a & = b
\end{aligned}$
C)
$\begin{aligned}
| a - 5 | & = | b - 5 | \
a + 5 & = 5 - b \quad ; \text { not one-to-one } \
a & = - b
\end{aligned}$
D)
$\begin{aligned}
| a - 5 | & = | b - 5 | \
| - 5 | - a & = | - 5 | + b ; \text { not one-to-one }
\end{aligned}$
E)
$\begin{aligned}
- a & = b \
| a - 5 | & = | b - 5 | \
| - 5 | - a & = | - 5 | - b ; \text { one-to-one } \
- a & = - b \
a & = b
\end{aligned}$

Accepted Answer

For a function to be one-to-one, each input must map to a unique output. The correct algebraic manipulation for the given function $| x - 5 |, \quad x \leq 5$ is shown in option A. When $x \leq 5$, the expression $| x - 5 |$ simplifies to $5 - x$ because the input values are less than or equal to 5, making the expression inside the absolute value negative or zero. The algebraic steps in A correctly show that if $| a - 5 | = | b - 5 |$, then $a = b$, indicating that the function is one-to-one within the specified domain.

Question 15

Evaluate the following function for $f ( x ) = - 2 x ^ { 2 } + 1$ and $g ( x ) = x + 4$ algebraically.
$\left( \frac { f } { g } \right) ( q - 4 )$
A) $\frac { - 2 q ^ { 2 } + 5 } { q + 8 }$
B) $\frac { - 2 q ^ { 2 } + 8 q - 31 } { q }$
C) $\frac { - 2 q ^ { 2 } + 5 } { q }$
D) $\frac { - 2 q ^ { 2 } + 16 q - 31 } { q }$
E) $\frac { - 2 q ^ { 2 } - 3 } { q }$

Accepted Answer

The answer of Evaluate the following function for \(f (...

Question 16

Evaluate the following function at the specified value of the independent variable and simplify.
$$f ( w ) = \frac { - 7 w ^ { 2 } + 20 } { w ^ { 2 } } ; \quad f ( 0 )$$
A) 20
B) 0
C) $- 7$
D) 13
E) undefined

Accepted Answer

The function $f(w) = \frac{-7w^2 + 20}{w^2}$ becomes undefined at $w = 0$ because it results in a division by zero.

Question 17

Write the slope-intercept form of the equation of the line through the given point perpendicular to the given line.
point: $( - 4,7 )$
line: $- 5 x - 15 y = - 6$
A) $y = \frac { 1 } { 5 } x + \frac { 39 } { 5 }$
B) $y = - \frac { 1 } { 3 } x + \frac { 17 } { 3 }$
C) $y = 3 x + 19$
D) $y = - 5 x + 27$
E) $y = 3 x - \frac { 5 } { 3 }$

Accepted Answer

The answer of Write the slope-intercept form of the equation...

Question 18

Find the domain of the function.
$f ( y ) = \sqrt { 9 - y ^ { 2 } }$
A) $- 3 \leq y \leq 3$
B) $y \leq - 3$ or $y \geq 3$
C) $y \geq 0$
D) $y \leq 3$
E) all real numbers

Accepted Answer

The domain of $f(y) = \sqrt{9 - y^2}$ consists of all values of $y$ for which the expression under the square root, $9 - y^2$, is greater than or equal to 0. Solving the inequality $9 - y^2 \geq 0$ leads to $(-3 \leq y) \land (y \leq 3)$, which corresponds to option A: $-3 \leq y \leq 3$.

Question 19

Find $( f g ) ( x )$.
$$f ( x ) = \sqrt { - 5 x } \quad g ( x ) = \sqrt { - 8 x + 6 }$$
A) $( f g ) ( x ) = 2 x \sqrt { 10 } - \sqrt { 30 x }$
B) $( f g ) ( x ) = 2 x \sqrt { 10 - 30 x }$
C) $( f g ) ( x ) = \sqrt { - 13 x + 6 }$
D) $( f g ) ( x ) = \sqrt { 40 x ^ { 2 } + 6 }$
E) $( f g ) ( x ) = \sqrt { 40 x ^ { 2 } - 30 x }$

Accepted Answer

To find $(fg)(x)$, we substitute $g(x)$ into $f(x)$, resulting in $f(g(x)) = \sqrt{-5(\sqrt{-8x + 6})}$. However, this simplification is incorrect. The correct approach is to apply $f$ to $g(x)$ directly, which means we should compute $f(g(x))$ correctly. Since there's a misunderstanding in the simplification process, let's correct the approach: $(fg)(x) = f(g(x)) = \sqrt{-5(\sqrt{-8x + 6})}$ is not the right interpretation of function composition here. Instead, we should apply $g(x)$ into $f(x)$ correctly, but the provided explanation mistakenly suggests an incorrect substitution and simplification process. The correct process involves substituting $g(x)$ into $f(x)$ properly, which actually means calculating $f(g(x))$ as $f(\sqrt{-8x + 6})$, but this explanation does not directly lead to any of the given options correctly due to a misinterpretation of how to perform function composition. The correct method involves calculating the composition of $f$ and $g$ without the incorrect substitution error, leading to the correct answer by properly applying the definition of function composition.

Question 20

Given the following function, $h ( x )$, find two functions $f$ and $g$ such that $( f \circ g ) ( x ) = h ( x )$.
$h ( x ) = \sqrt [ 3 ] { x ^ { 2 } - 11 }$
A) $f ( x ) = \sqrt [ 3 ] { x ^ { 2 } } , g ( x ) = - 11$
B) $f ( x ) = \sqrt [ 3 ] { x ^ { 2 } } , g ( x ) = x - 11$
C) $f ( x ) = \sqrt [ 3 ] { x } , g ( x ) = x - 11$
D) $f ( x ) = \sqrt [ 3 ] { x - 11 } , g ( x ) = x ^ { 2 }$
E) $f ( x ) = \sqrt [ 3 ] { x - 11 } , \quad g ( x ) = x + 11$

Accepted Answer

Function $f(x) = \sqrt[3]{x - 11}$ and $g(x) = x^2$ work together because when $g(x) = x^2$ is substituted into $f(x)$, it results in $f(g(x)) = \sqrt[3]{x^2 - 11}$, which matches $h(x)$.

Quiz 1: Functions and Their Graphs

Determine an equation that may represented by the graph shown below. $Determine an equation that may represented by the graph shown below. A) f ( x ) = | x + 1 | - 1 B) f ( x ) = | x - 1 | + 1 C) f ( x ) = | x + 1 | + 1 D) f ( x ) = | x - 1 | - 1 E) \quad f ( x ) = - | x - 1 | + 1$

The scatter plots of different data are shown below. Determine whether there is a positive correlation, negative correlation, or no discernible correlation between the variables.

Which equation does not represent $y$ as a function of $x$ ?

Find the slope-intercept form of the line passing through the points. $( - 1 , - 6 ) , ( 0 , - 2 )$

Determine the domain and range of the inverse function $f ^ { - 1 }$ of the following function $f$ . $f ( x ) = - | x + 6 | + 2$ , where $x > - 6$

Use function notation to write $g$ in terms of $f ( x ) = x ^ { 3 }$ . $g ( x ) = - \frac { 1 } { 5 } ( x + 4 ) ^ { 3 }$

Find the difference quotient and simplify your answer. $f ( w ) = - 9 w ^ { 2 } + 2 w , \quad \frac { f ( 4 + h ) - f ( 4 ) } { h } , h \neq 0$

Determine the domain of $g ( x ) = \frac { 1 } { x ^ { 2 } - 49 }$ .

If $f$ is an even function, determine if $g$ is even, odd, or neither. $g ( x ) = - f ( x - 2 )$

Evaluate the function at the specified value of the independent variable and simplify. $\begin{array} { l } q ( p ) = \frac { - 2 p } { 5 p - 2 } \\q ( x - 9 ) \end{array}$

Compare the graph of the following function with the graph of $f ( x ) = | x |$ . $y = \left| \frac { 4 } { 9 } x \right|$

Determine algebraically whether the following function is one-to-one $| x - 5 | , \quad x \leq 5$

Evaluate the following function for $f ( x ) = - 2 x ^ { 2 } + 1$ and $g ( x ) = x + 4$ algebraically. $\left( \frac { f } { g } \right) ( q - 4 )$

Evaluate the following function at the specified value of the independent variable and simplify. $f ( w ) = \frac { - 7 w ^ { 2 } + 20 } { w ^ { 2 } } ; \quad f ( 0 )$

Write the slope-intercept form of the equation of the line through the given point perpendicular to the given line. point: $( - 4,7 )$ line: $- 5 x - 15 y = - 6$

Find the domain of the function. $f ( y ) = \sqrt { 9 - y ^ { 2 } }$

Find $( f g ) ( x )$ . $f ( x ) = \sqrt { - 5 x } \quad g ( x ) = \sqrt { - 8 x + 6 }$

Given the following function, $h ( x )$ , find two functions $f$ and $g$ such that $( f \circ g ) ( x ) = h ( x )$ . $h ( x ) = \sqrt [ 3 ] { x ^ { 2 } - 11 }$

Quiz 1: Functions and Their Graphs

Determine an equation that may represented by the graph shown below.

The scatter plots of different data are shown below. Determine whether there is a positive correlation, negative correlation, or no discernible correlation between the variables.

Which equation does not represent yyy as a function of xxx ?

Find the slope-intercept form of the line passing through the points. (−1,−6) ,(0,−2) ( - 1 , - 6 ) , ( 0 , - 2 ) (−1,−6) ,(0,−2)

Determine the domain and range of the inverse function f−1f ^ { - 1 }f−1 of the following function fff . f(x) =−∣x+6∣+2f ( x ) = - | x + 6 | + 2f(x) =−∣x+6∣+2 , where x>−6x > - 6x>−6

Use function notation to write ggg in terms of f(x) =x3f ( x ) = x ^ { 3 }f(x) =x3 . g(x) =−15(x+4) 3g ( x ) = - \frac { 1 } { 5 } ( x + 4 ) ^ { 3 }g(x) =−51​(x+4) 3

Find the difference quotient and simplify your answer. f(w) =−9w2+2w,f(4+h) −f(4) h,h≠0f ( w ) = - 9 w ^ { 2 } + 2 w , \quad \frac { f ( 4 + h ) - f ( 4 ) } { h } , h \neq 0f(w) =−9w2+2w,hf(4+h) −f(4) ​,h=0

Determine the domain of g(x) =1x2−49g ( x ) = \frac { 1 } { x ^ { 2 } - 49 }g(x) =x2−491​ .

If fff is an even function, determine if ggg is even, odd, or neither. g(x) =−f(x−2) g ( x ) = - f ( x - 2 ) g(x) =−f(x−2)

Evaluate the function at the specified value of the independent variable and simplify. q(p) =−2p5p−2q(x−9) \begin{array} { l } q ( p ) = \frac { - 2 p } { 5 p - 2 } \\q ( x - 9 ) \end{array}q(p) =5p−2−2p​q(x−9) ​

Compare the graph of the following function with the graph of f(x) =∣x∣f ( x ) = | x |f(x) =∣x∣ . y=∣49x∣y = \left| \frac { 4 } { 9 } x \right|y=​94​x​

Use the graph of f(x) =x2f ( x ) = x ^ { 2 }f(x) =x2 to write an equation for the function whose graph is shown.

Determine algebraically whether the following function is one-to-one ∣x−5∣,x≤5| x - 5 | , \quad x \leq 5∣x−5∣,x≤5

Evaluate the following function for f(x) =−2x2+1f ( x ) = - 2 x ^ { 2 } + 1f(x) =−2x2+1 and g(x) =x+4g ( x ) = x + 4g(x) =x+4 algebraically. (fg) (q−4) \left( \frac { f } { g } \right) ( q - 4 ) (gf​) (q−4)

Evaluate the following function at the specified value of the independent variable and simplify. f(w) =−7w2+20w2;f(0) f ( w ) = \frac { - 7 w ^ { 2 } + 20 } { w ^ { 2 } } ; \quad f ( 0 ) f(w) =w2−7w2+20​;f(0)

Write the slope-intercept form of the equation of the line through the given point perpendicular to the given line. point: (−4,7) ( - 4,7 ) (−4,7) line: −5x−15y=−6- 5 x - 15 y = - 6−5x−15y=−6

Find the domain of the function. f(y) =9−y2f ( y ) = \sqrt { 9 - y ^ { 2 } }f(y) =9−y2​

Find (fg) (x) ( f g ) ( x ) (fg) (x) . f(x) =−5xg(x) =−8x+6f ( x ) = \sqrt { - 5 x } \quad g ( x ) = \sqrt { - 8 x + 6 }f(x) =−5x​g(x) =−8x+6​

Given the following function, h(x) h ( x ) h(x) , find two functions fff and ggg such that (f∘g) (x) =h(x) ( f \circ g ) ( x ) = h ( x ) (f∘g) (x) =h(x) . h(x) =x2−113h ( x ) = \sqrt [ 3 ] { x ^ { 2 } - 11 }h(x) =3x2−11​

Determine an equation that may represented by the graph shown below. $Determine an equation that may represented by the graph shown below. A) f ( x ) = | x + 1 | - 1 B) f ( x ) = | x - 1 | + 1 C) f ( x ) = | x + 1 | + 1 D) f ( x ) = | x - 1 | - 1 E) \quad f ( x ) = - | x - 1 | + 1$

Which equation does not represent $y$ as a function of $x$ ?

Find the slope-intercept form of the line passing through the points. $( - 1 , - 6 ) , ( 0 , - 2 )$

Determine the domain and range of the inverse function $f ^ { - 1 }$ of the following function $f$ . $f ( x ) = - | x + 6 | + 2$ , where $x > - 6$

Use function notation to write $g$ in terms of $f ( x ) = x ^ { 3 }$ . $g ( x ) = - \frac { 1 } { 5 } ( x + 4 ) ^ { 3 }$

Find the difference quotient and simplify your answer. $f ( w ) = - 9 w ^ { 2 } + 2 w , \quad \frac { f ( 4 + h ) - f ( 4 ) } { h } , h \neq 0$

Determine the domain of $g ( x ) = \frac { 1 } { x ^ { 2 } - 49 }$ .

If $f$ is an even function, determine if $g$ is even, odd, or neither. $g ( x ) = - f ( x - 2 )$

Evaluate the function at the specified value of the independent variable and simplify. $\begin{array} { l } q ( p ) = \frac { - 2 p } { 5 p - 2 } \\q ( x - 9 ) \end{array}$

Compare the graph of the following function with the graph of $f ( x ) = | x |$ . $y = \left| \frac { 4 } { 9 } x \right|$

Determine algebraically whether the following function is one-to-one $| x - 5 | , \quad x \leq 5$

Evaluate the following function for $f ( x ) = - 2 x ^ { 2 } + 1$ and $g ( x ) = x + 4$ algebraically. $\left( \frac { f } { g } \right) ( q - 4 )$

Evaluate the following function at the specified value of the independent variable and simplify. $f ( w ) = \frac { - 7 w ^ { 2 } + 20 } { w ^ { 2 } } ; \quad f ( 0 )$

Write the slope-intercept form of the equation of the line through the given point perpendicular to the given line. point: $( - 4,7 )$ line: $- 5 x - 15 y = - 6$

Find the domain of the function. $f ( y ) = \sqrt { 9 - y ^ { 2 } }$

Find $( f g ) ( x )$ . $f ( x ) = \sqrt { - 5 x } \quad g ( x ) = \sqrt { - 8 x + 6 }$

Given the following function, $h ( x )$ , find two functions $f$ and $g$ such that $( f \circ g ) ( x ) = h ( x )$ . $h ( x ) = \sqrt [ 3 ] { x ^ { 2 } - 11 }$