Question 1

For the given functions f(x) and g(x), find (f + g)(x) or (f - g)(x) as indicated
-$f(x)=7 x-3, g(x)=4 x-7$
Find $(f+g)(x)$.
A) $-3 \mathrm{x}-4$
B) $11 x+4$
C) $11 \mathrm{x}-10$
D) $3 \mathrm{x}-10$

Accepted Answer

To find $(f+g)(x)$, you add the functions $f(x) = 7x - 3$ and $g(x) = 4x - 7$ together: $7x - 3 + 4x - 7 = 11x - 10$.

Question 2

For the given functions f(x) and g(x), find (f + g)(x) or (f - g)(x) as indicated
-$f(x)=-7 x+5, g(x)=-2 x+7$
Find $(f+g)(x)$.
A) $-9 x+12$
B) $-5 \mathrm{x}+12$
C) $-2 \mathrm{x}+5$
D) $3 \mathrm{x}$

Accepted Answer

(f+g)(x) = f(x) + g(x) = (-7x + 5) + (-2x + 7) = -9x + 12

Question 3

For the given functions f(x) and g(x), find (f + g)(x) or (f - g)(x) as indicated
-$f(x)=-5 x+8, g(x)=x^{2}-3 x-9$
Find $(f+g)(x)$.
A) $x^{2}+3 x-1$
B) $x^{2}-8 x-1$
C) $x^{2}-8 x+12$
D) $x^{2}+3 x+5$

Accepted Answer

B

Question 4

For the given functions f(x) and g(x), find (f + g)(x) or (f - g)(x) as indicated
-$f(x)=2 x^{2}+7 x-5, g(x)=7 x^{2}+3 x+9$
Find $(f+g)(x)$.
A) $-9 x^{2}+10 x+4$
B) $2 x^{2}+5 x+4$
C) $23 x^{2}$
D) $9 x^{2}+10 x+4$

Accepted Answer

To find $(f+g)(x)$, you add the corresponding coefficients of $f(x)$ and $g(x)$: $2x^2 + 7x^2 = 9x^2$, $7x + 3x = 10x$, and $-5 + 9 = 4$, resulting in $9x^2 + 10x + 4$.

Question 5

For the given functions f(x) and g(x), find (f + g)(x) or (f - g)(x) as indicated
-$f(x)=5 x-6, g(x)=2 x-4$
Find $(f-g)(x)$.
A) $7 \mathrm{x}-10$
B) $-3 x+2$
C) $3 x-2$
D) $3 x-10$

Accepted Answer

$(f-g)(x) = (5x-6) - (2x-4) = 5x - 6 - 2x + 4 = 3x - 2$.

Question 6

For the given functions f(x) and g(x), find (f + g)(x) or (f - g)(x) as indicated
-$f(x)=-8 x+8, g(x)=-5 x+9$
Find $(\mathrm{f}-\mathrm{g})(\mathrm{x})$.
A) $3 \mathrm{x}$
B) $-13 x-1$
C) $-3 x-1$
D) $-3 x+16$

Accepted Answer

The answer of For the given functions f(x) and g(x),...

Question 7

For the given functions f(x) and g(x), find (f + g)(x) or (f - g)(x) as indicated
-$f(x)=-5 x^{2}-18 x, g(x)=-11 x^{2}-20 x+3$
Find $(f-g)(x)$.
A) $6 x^{2}-38 x-3$
B) $-16 x^{2}-38 x+3$
C) $8 x^{2}-3$
D) $6 x^{2}+2 x-3$

Accepted Answer

The answer of For the given functions f(x) and g(x),...

Question 8

For the given functions $f(x)$ and $g(x)$, find $(f \cdot g)(x)$ or $\left(\frac{f}{g}\right)(x)$ as indicated.
-$f(x)=x+4, g(x)=x+7$
Find $(f \cdot g)(x)$.
A) $x^{2}+11 x+11$
B) $x^{2}+8 x+28$
C) $x^{2}+11 x+28$
D) $x^{2}+28$

Accepted Answer

To find $(f \cdot g)(x)$, you multiply $f(x)$ by $g(x)$: $(x+4)(x+7) = x^2 + 7x + 4x + 28 = x^2 + 11x + 28$.

Question 9

For the given functions $f(x)$ and $g(x)$, find $(f \cdot g)(x)$ or $\left(\frac{f}{g}\right)(x)$ as indicated.
-$f(x)=2 x-8, g(x)=7 x-3$
Find $(f \cdot g)(x)$.
A) $14 x^{2}-59 x+24$
B) $14 x^{2}+24$
C) $14 x^{2}-62 x+24$
D) $9 x^{2}-62 x-11$

Accepted Answer

The answer of For the given functions $f(x)$ and $g(x)$,...

Question 10

For the given functions $f(x)$ and $g(x)$, find $(f \cdot g)(x)$ or $\left(\frac{f}{g}\right)(x)$ as indicated.
-$f(x)=-2 x, g(x)=10 x-5$
Find $(f \cdot g)(x)$.
A) $10 x^{2}+10 x$
B) $-10 x^{2}$
C) $-20 x^{2}+10 x$
D) $-20 x^{2}-5$

Accepted Answer

The answer of For the given functions $f(x)$ and $g(x)$,...

Question 11

For the given functions $f(x)$ and $g(x)$, find $(f \cdot g)(x)$ or $\left(\frac{f}{g}\right)(x)$ as indicated.
-$f(x)=-9 x+4, g(x)=5 x^{2}-x+4$
Find $(\mathrm{f} \cdot \mathrm{g})(\mathrm{x})$.
A) $-45 x^{3}-40 x+16$
B) $-45 x^{3}+11 x^{2}-40 x+16$
C) $14 x^{2}-40 x+16$
D) $-45 x^{3}+29 x^{2}-40 x+16$

Accepted Answer

To find $(f \cdot g)(x)$, you multiply $f(x)$ by $g(x)$: $(-9x + 4) \cdot (5x^2 - x + 4)$. Distributing gives: $-45x^3 + 9x^2 - 16x + 20x^2 - 4x + 16$, which simplifies to $-45x^3 + 29x^2 - 40x + 16$.

Question 12

For the given functions $f(x)$ and $g(x)$, find $(f \cdot g)(x)$ or $\left(\frac{f}{g}\right)(x)$ as indicated.
-$f(x)=4 x^{2}+2 x+4, g(x)=x^{2}-4 x+5$
Find $(f \cdot g)(x)$.
A) $4 x^{4}-16 x^{3}+12 x^{2}-6 x+20$
B) $4 x^{4}-16 x^{3}+16 x^{2}-6 x+20$
C) $4 x^{4}-14 x^{3}+16 x^{2}-6 x+20$
D) $4 x^{4}-14 x^{3}+12 x^{2}-6 x+20$

Accepted Answer

The answer of For the given functions $f(x)$ and $g(x)$,...

Question 13

For the given functions $f(x)$ and $g(x)$, find $(f \cdot g)(x)$ or $\left(\frac{f}{g}\right)(x)$ as indicated.
-$f(x)=2 x+1, g(x)=x-7$
Find $\left(\frac{f}{g}\right)(x)$.

A) $\frac{2 x+1}{x-7}$

B) $\frac{x-7}{2 x+1}$

C) $2-\frac{x}{7}$

D) $2 x-\frac{1}{7}$

Accepted Answer

The operation indicated is division, so $\left(\frac{f}{g}\right)(x) = \frac{f(x)}{g(x)} = \frac{2x+1}{x-7}$.

Question 14

For the given functions $f(x)$ and $g(x)$, find $(f \cdot g)(x)$ or $\left(\frac{f}{g}\right)(x)$ as indicated.
-$f(x)=x+4, g(x)=2 x-7$
Find $\left(\frac{f}{g}\right)(x)$.
A) $\frac{2 x-7}{x+4}$

B) $\frac{x}{2}-\frac{4}{7}$

C) $\frac{x+4}{2 x-7}$

D) $\frac{x}{2 x-7}+4$

Accepted Answer

The operation $\left(\frac{f}{g}\right)(x)$ means dividing $f(x)$ by $g(x)$, so $\left(\frac{f}{g}\right)(x) = \frac{x+4}{2x-7}$.

Question 15

For the given functions $f(x)$ and $g(x)$, find $(f \cdot g)(x)$ or $\left(\frac{f}{g}\right)(x)$ as indicated.
-$f(x)=x^{2}+8 x+12, g(x)=x+6$
Find $\left(\frac{f}{g}\right)(x)$.
A) $x+2$
B) $x^{2}+2$
C) $x-6$
D) $x^{3}-6$

Accepted Answer

To find $\left(\frac{f}{g}\right)(x)$, we divide $f(x)$ by $g(x)$: $\frac{x^{2}+8x+12}{x+6}$. Factoring the numerator gives $(x+6)(x+2)$. Dividing by $x+6$ leaves $x+2$.

Question 16

For the given functions $f(x)$ and $g(x)$, find $(f \cdot g)(x)$ or $\left(\frac{f}{g}\right)(x)$ as indicated.
-$f(x)=x^{2}+2 x-15, g(x)=x+5$
Find $\left(\frac{f}{g}\right)(x)$.
A) $\mathrm{x}-3$
B) $x^{2}+3 x-10$
C) $x+3$
D) $x^{2}-3$

Accepted Answer

To find $\left(\frac{f}{g}\right)(x)$, divide $f(x)$ by $g(x)$: $\frac{x^2 + 2x - 15}{x + 5}$. The division results in $x - 3$ with no remainder.

Question 17

Solve the problem.
-Find $(f+g)(4)$ when $f(x)=x+7$ and $g(x)=x+1$.
A) 0
B) 14
C) 16
D) 2

Accepted Answer

To find $(f+g)(4)$, we first find $f(4) = 4 + 7 = 11$ and $g(4) = 4 + 1 = 5$. Adding these together gives $11 + 5 = 16$.

Question 18

Solve the problem.
-Find $(f+g)(-2)$ when $f(x)=-2 x^{3}-3 x-35$ and $g(x)=5 x^{2}+2 x$
A) 3
B) -7
C) -27
D) -9

Accepted Answer

The answer of Solve the problem.
-Find $(f+g)(-2)$ when \(f(x)=-2 x^{3}-3...

Question 19

Solve the problem.
-Find (f - g)(4) when $f(x)=3 x^{2}+5$ and $g(x)=x+1$.
A) 56
B) 50
C) -57
D) 48

Accepted Answer

The answer of Solve the problem.
-Find (f - g)(4) when...

Question 20

Solve the problem.
-Find $(f \cdot g)(2)$ when $f(x)=x-6$ and $g(x)=-3 x^{2}+12 x-4$.
A) -96
B) -32
C) 64
D) -128

Accepted Answer

The answer of Solve the problem.
-Find $(f \cdot g)(2)$ when...

Quiz 9: Logarithmic and Exponential Functions

For the given functions f(x) and g(x) , find (f + g) (x) or (f - g) (x) as indicated - $f(x) =7 x-3, g(x) =4 x-7$ Find $(f+g) (x)$ .

For the given functions f(x) and g(x) , find (f + g) (x) or (f - g) (x) as indicated - $f(x) =-7 x+5, g(x) =-2 x+7$ Find $(f+g) (x)$ .

For the given functions f(x) and g(x) , find (f + g) (x) or (f - g) (x) as indicated - $f(x) =-5 x+8, g(x) =x^{2}-3 x-9$ Find $(f+g) (x)$ .

For the given functions f(x) and g(x) , find (f + g) (x) or (f - g) (x) as indicated - $f(x) =2 x^{2}+7 x-5, g(x) =7 x^{2}+3 x+9$ Find $(f+g) (x)$ .

For the given functions f(x) and g(x) , find (f + g) (x) or (f - g) (x) as indicated - $f(x) =5 x-6, g(x) =2 x-4$ Find $(f-g) (x)$ .

For the given functions f(x) and g(x) , find (f + g) (x) or (f - g) (x) as indicated - $f(x) =-8 x+8, g(x) =-5 x+9$ Find $(\mathrm{f}-\mathrm{g}) (\mathrm{x})$ .

For the given functions f(x) and g(x) , find (f + g) (x) or (f - g) (x) as indicated - $f(x) =-5 x^{2}-18 x, g(x) =-11 x^{2}-20 x+3$ Find $(f-g) (x)$ .

For the given functions $f(x)$ and $g(x)$ , find $(f \cdot g) (x)$ or $\left(\frac{f}{g}\right) (x)$ as indicated. - $f(x) =x+4, g(x) =x+7$ Find $(f \cdot g) (x)$ .

For the given functions $f(x)$ and $g(x)$ , find $(f \cdot g) (x)$ or $\left(\frac{f}{g}\right) (x)$ as indicated. - $f(x) =2 x-8, g(x) =7 x-3$ Find $(f \cdot g) (x)$ .

For the given functions $f(x)$ and $g(x)$ , find $(f \cdot g) (x)$ or $\left(\frac{f}{g}\right) (x)$ as indicated. - $f(x) =-2 x, g(x) =10 x-5$ Find $(f \cdot g) (x)$ .

For the given functions $f(x)$ and $g(x)$ , find $(f \cdot g) (x)$ or $\left(\frac{f}{g}\right) (x)$ as indicated. - $f(x) =-9 x+4, g(x) =5 x^{2}-x+4$ Find $(\mathrm{f} \cdot \mathrm{g}) (\mathrm{x})$ .

For the given functions $f(x)$ and $g(x)$ , find $(f \cdot g) (x)$ or $\left(\frac{f}{g}\right) (x)$ as indicated. - $f(x) =4 x^{2}+2 x+4, g(x) =x^{2}-4 x+5$ Find $(f \cdot g) (x)$ .

For the given functions $f(x)$ and $g(x)$ , find $(f \cdot g) (x)$ or $\left(\frac{f}{g}\right) (x)$ as indicated. - $f(x) =2 x+1, g(x) =x-7$ Find $\left(\frac{f}{g}\right) (x)$ .

For the given functions $f(x)$ and $g(x)$ , find $(f \cdot g) (x)$ or $\left(\frac{f}{g}\right) (x)$ as indicated. - $f(x) =x+4, g(x) =2 x-7$ Find $\left(\frac{f}{g}\right) (x)$ .

For the given functions $f(x)$ and $g(x)$ , find $(f \cdot g) (x)$ or $\left(\frac{f}{g}\right) (x)$ as indicated. - $f(x) =x^{2}+8 x+12, g(x) =x+6$ Find $\left(\frac{f}{g}\right) (x)$ .

For the given functions $f(x)$ and $g(x)$ , find $(f \cdot g) (x)$ or $\left(\frac{f}{g}\right) (x)$ as indicated. - $f(x) =x^{2}+2 x-15, g(x) =x+5$ Find $\left(\frac{f}{g}\right) (x)$ .

Solve the problem. -Find $(f+g) (4)$ when $f(x) =x+7$ and $g(x) =x+1$ .

Solve the problem. -Find $(f+g) (-2)$ when $f(x) =-2 x^{3}-3 x-35$ and $g(x) =5 x^{2}+2 x$

Solve the problem. -Find (f - g) (4) when $f(x) =3 x^{2}+5$ and $g(x) =x+1$ .

Solve the problem. -Find $(f \cdot g) (2)$ when $f(x) =x-6$ and $g(x) =-3 x^{2}+12 x-4$ .

Quiz 9: Logarithmic and Exponential Functions

For the given functions f(x) and g(x) , find (f + g) (x) or (f - g) (x) as indicated - f(x) =7x−3,g(x) =4x−7f(x) =7 x-3, g(x) =4 x-7f(x) =7x−3,g(x) =4x−7 Find (f+g) (x) (f+g) (x) (f+g) (x) .

For the given functions f(x) and g(x) , find (f + g) (x) or (f - g) (x) as indicated - f(x) =−7x+5,g(x) =−2x+7f(x) =-7 x+5, g(x) =-2 x+7f(x) =−7x+5,g(x) =−2x+7 Find (f+g) (x) (f+g) (x) (f+g) (x) .

For the given functions f(x) and g(x) , find (f + g) (x) or (f - g) (x) as indicated - f(x) =−5x+8,g(x) =x2−3x−9f(x) =-5 x+8, g(x) =x^{2}-3 x-9f(x) =−5x+8,g(x) =x2−3x−9 Find (f+g) (x) (f+g) (x) (f+g) (x) .

For the given functions f(x) and g(x) , find (f + g) (x) or (f - g) (x) as indicated - f(x) =2x2+7x−5,g(x) =7x2+3x+9f(x) =2 x^{2}+7 x-5, g(x) =7 x^{2}+3 x+9f(x) =2x2+7x−5,g(x) =7x2+3x+9 Find (f+g) (x) (f+g) (x) (f+g) (x) .

For the given functions f(x) and g(x) , find (f + g) (x) or (f - g) (x) as indicated - f(x) =5x−6,g(x) =2x−4f(x) =5 x-6, g(x) =2 x-4f(x) =5x−6,g(x) =2x−4 Find (f−g) (x) (f-g) (x) (f−g) (x) .

For the given functions f(x) and g(x) , find (f + g) (x) or (f - g) (x) as indicated - f(x) =−8x+8,g(x) =−5x+9f(x) =-8 x+8, g(x) =-5 x+9f(x) =−8x+8,g(x) =−5x+9 Find (f−g) (x) (\mathrm{f}-\mathrm{g}) (\mathrm{x}) (f−g) (x) .

For the given functions f(x) and g(x) , find (f + g) (x) or (f - g) (x) as indicated - f(x) =−5x2−18x,g(x) =−11x2−20x+3f(x) =-5 x^{2}-18 x, g(x) =-11 x^{2}-20 x+3f(x) =−5x2−18x,g(x) =−11x2−20x+3 Find (f−g) (x) (f-g) (x) (f−g) (x) .

For the given functions f(x) f(x) f(x) and g(x) g(x) g(x) , find (f⋅g) (x) (f \cdot g) (x) (f⋅g) (x) or (fg) (x) \left(\frac{f}{g}\right) (x) (gf​) (x) as indicated. - f(x) =x+4,g(x) =x+7f(x) =x+4, g(x) =x+7f(x) =x+4,g(x) =x+7 Find (f⋅g) (x) (f \cdot g) (x) (f⋅g) (x) .

For the given functions f(x) f(x) f(x) and g(x) g(x) g(x) , find (f⋅g) (x) (f \cdot g) (x) (f⋅g) (x) or (fg) (x) \left(\frac{f}{g}\right) (x) (gf​) (x) as indicated. - f(x) =2x−8,g(x) =7x−3f(x) =2 x-8, g(x) =7 x-3f(x) =2x−8,g(x) =7x−3 Find (f⋅g) (x) (f \cdot g) (x) (f⋅g) (x) .

For the given functions f(x) f(x) f(x) and g(x) g(x) g(x) , find (f⋅g) (x) (f \cdot g) (x) (f⋅g) (x) or (fg) (x) \left(\frac{f}{g}\right) (x) (gf​) (x) as indicated. - f(x) =−2x,g(x) =10x−5f(x) =-2 x, g(x) =10 x-5f(x) =−2x,g(x) =10x−5 Find (f⋅g) (x) (f \cdot g) (x) (f⋅g) (x) .

For the given functions f(x) f(x) f(x) and g(x) g(x) g(x) , find (f⋅g) (x) (f \cdot g) (x) (f⋅g) (x) or (fg) (x) \left(\frac{f}{g}\right) (x) (gf​) (x) as indicated. - f(x) =2x+1,g(x) =x−7f(x) =2 x+1, g(x) =x-7f(x) =2x+1,g(x) =x−7 Find (fg) (x) \left(\frac{f}{g}\right) (x) (gf​) (x) .

For the given functions f(x) f(x) f(x) and g(x) g(x) g(x) , find (f⋅g) (x) (f \cdot g) (x) (f⋅g) (x) or (fg) (x) \left(\frac{f}{g}\right) (x) (gf​) (x) as indicated. - f(x) =x+4,g(x) =2x−7f(x) =x+4, g(x) =2 x-7f(x) =x+4,g(x) =2x−7 Find (fg) (x) \left(\frac{f}{g}\right) (x) (gf​) (x) .

Solve the problem. -Find (f+g) (4) (f+g) (4) (f+g) (4) when f(x) =x+7f(x) =x+7f(x) =x+7 and g(x) =x+1g(x) =x+1g(x) =x+1 .

Solve the problem. -Find (f+g) (−2) (f+g) (-2) (f+g) (−2) when f(x) =−2x3−3x−35f(x) =-2 x^{3}-3 x-35f(x) =−2x3−3x−35 and g(x) =5x2+2xg(x) =5 x^{2}+2 xg(x) =5x2+2x

Solve the problem. -Find (f - g) (4) when f(x) =3x2+5f(x) =3 x^{2}+5f(x) =3x2+5 and g(x) =x+1g(x) =x+1g(x) =x+1 .

Solve the problem. -Find (f⋅g) (2) (f \cdot g) (2) (f⋅g) (2) when f(x) =x−6f(x) =x-6f(x) =x−6 and g(x) =−3x2+12x−4g(x) =-3 x^{2}+12 x-4g(x) =−3x2+12x−4 .

For the given functions f(x) and g(x) , find (f + g) (x) or (f - g) (x) as indicated - $f(x) =7 x-3, g(x) =4 x-7$ Find $(f+g) (x)$ .

For the given functions f(x) and g(x) , find (f + g) (x) or (f - g) (x) as indicated - $f(x) =-7 x+5, g(x) =-2 x+7$ Find $(f+g) (x)$ .

For the given functions f(x) and g(x) , find (f + g) (x) or (f - g) (x) as indicated - $f(x) =-5 x+8, g(x) =x^{2}-3 x-9$ Find $(f+g) (x)$ .

For the given functions f(x) and g(x) , find (f + g) (x) or (f - g) (x) as indicated - $f(x) =2 x^{2}+7 x-5, g(x) =7 x^{2}+3 x+9$ Find $(f+g) (x)$ .

For the given functions f(x) and g(x) , find (f + g) (x) or (f - g) (x) as indicated - $f(x) =5 x-6, g(x) =2 x-4$ Find $(f-g) (x)$ .

For the given functions f(x) and g(x) , find (f + g) (x) or (f - g) (x) as indicated - $f(x) =-8 x+8, g(x) =-5 x+9$ Find $(\mathrm{f}-\mathrm{g}) (\mathrm{x})$ .

For the given functions f(x) and g(x) , find (f + g) (x) or (f - g) (x) as indicated - $f(x) =-5 x^{2}-18 x, g(x) =-11 x^{2}-20 x+3$ Find $(f-g) (x)$ .

For the given functions $f(x)$ and $g(x)$ , find $(f \cdot g) (x)$ or $\left(\frac{f}{g}\right) (x)$ as indicated. - $f(x) =x+4, g(x) =x+7$ Find $(f \cdot g) (x)$ .

For the given functions $f(x)$ and $g(x)$ , find $(f \cdot g) (x)$ or $\left(\frac{f}{g}\right) (x)$ as indicated. - $f(x) =2 x-8, g(x) =7 x-3$ Find $(f \cdot g) (x)$ .

For the given functions $f(x)$ and $g(x)$ , find $(f \cdot g) (x)$ or $\left(\frac{f}{g}\right) (x)$ as indicated. - $f(x) =-2 x, g(x) =10 x-5$ Find $(f \cdot g) (x)$ .

For the given functions $f(x)$ and $g(x)$ , find $(f \cdot g) (x)$ or $\left(\frac{f}{g}\right) (x)$ as indicated. - $f(x) =2 x+1, g(x) =x-7$ Find $\left(\frac{f}{g}\right) (x)$ .

For the given functions $f(x)$ and $g(x)$ , find $(f \cdot g) (x)$ or $\left(\frac{f}{g}\right) (x)$ as indicated. - $f(x) =x+4, g(x) =2 x-7$ Find $\left(\frac{f}{g}\right) (x)$ .

Solve the problem. -Find $(f+g) (4)$ when $f(x) =x+7$ and $g(x) =x+1$ .

Solve the problem. -Find $(f+g) (-2)$ when $f(x) =-2 x^{3}-3 x-35$ and $g(x) =5 x^{2}+2 x$

Solve the problem. -Find (f - g) (4) when $f(x) =3 x^{2}+5$ and $g(x) =x+1$ .

Solve the problem. -Find $(f \cdot g) (2)$ when $f(x) =x-6$ and $g(x) =-3 x^{2}+12 x-4$ .