Decide whether or not the functions are inverses of each other.
-$$f ( x ) = 4 x + 16 , g ( x ) = \frac { 1 } { 4 } x - 4$$
A) $Y e s$
B) $\mathrm { No }$

Question

Quizplus · Accepted Answer

To determine if $f(x)$ and $g(x)$ are inverses, we can check if $f(g(x)) = x$ and $g(f(x)) = x$. For $f(g(x))$, substitute $g(x)$ into $f(x)$: $f(g(x)) = 4(\frac{1}{4}x - 4) + 16 = x - 16 + 16 = x$. For $g(f(x))$, substitute $f(x)$ into $g(x)$: $g(f(x)) = \frac{1}{4}(4x + 16) - 4 = x + 4 - 4 = x$. Since both compositions return $x$, $f(x)$ and $g(x)$ are inverses of each other.

Decide Whether or Not the Functions Are Inverses of Each f(x)=4x+16,g(x)=14x−4f ( x ) = 4 x + 16 , g ( x ) = \frac { 1 } { 4 } x - 4f(x)=4x+16,g(x)=41​x−4

Decide Whether or Not the Functions Are Inverses of Each $f ( x ) = 4 x + 16 , g ( x ) = \frac { 1 } { 4 } x - 4$