For the given functions f and g , find the indicated composition.
-$$\begin{array} { l }
f ( x ) = \frac { x - 8 } { 3 } , \quad g ( x ) = 3 x + 8 \
( g f ) ( x )
\end{array}$$
A) $x - \frac { 8 } { 3 }$
B) $x + 16$
C) $x$
D) $3 x + 16$

Question

For the given functions f and g , find the indicated composition.
-$$\begin{array} { l } 
f ( x ) = \frac { x - 8 } { 3 } , \quad g ( x ) = 3 x + 8 \
( g f ) ( x )
\end{array}$$
A) $x - \frac { 8 } { 3 }$
B) $x + 16$
C) $x$
D) $3 x + 16$

Quizplus · Accepted Answer

To find the composition $(g \circ f)(x)$, we substitute $f(x)$ into $g(x)$. So, $g(f(x)) = g\left(\frac{x - 8}{3}\right) = 3\left(\frac{x - 8}{3}\right) + 8$. Simplifying this gives $x - 8 + 8 = x$, which matches choice C.

For the Given Functions F and G , Find the Indicated