Use function notation to write $g$ in terms of $f ( x ) = \sqrt { x }$. $g ( x ) = - \frac { 1 } { 3 } \sqrt { x - 8 } + 7$
A) $g ( x ) = - f ( x - 8 ) + 6$
B) $\quad g ( x ) = - \frac { 1 } { 3 } f ( x ) - 1$
C)
$g ( x ) = - \frac { 1 } { 3 } f ( x - 8 ) + 7$
D) $g ( x ) = f ( x ) + 7$
E) $\quad g ( x ) = f ( x - 8 ) - \frac { 7 } { 3 }$

Question

Quizplus · Accepted Answer

To write $g$ in terms of $f(x) = \sqrt{x}$, we can substitute $\sqrt{x}$ for $f(x)$ in the expression for $g(x)$:
$$g(x) = -\frac{1}{3}\sqrt{x-8} + 7$$
$$= -\frac{1}{3}f(x-8) + 7$$
Therefore, the correct choice is $\boxed{\textbf{(C)}}.$

Use Function Notation to Write ggg In Terms Of f(x)=xf ( x ) = \sqrt { x }f(x)=x​

Use Function Notation to Write $g$ In Terms Of $f ( x ) = \sqrt { x }$