Determine whether the given functions are inverses of each other.
-$$f ( x ) = \frac { x - 4 } { 4 } , \quad g ( x ) = 4 x + 4$$
A)Yes
B)No

Question

Quizplus · Accepted Answer

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

Determine Whether the Given Functions Are Inverses of Each Other f(x)=x−44,g(x)=4x+4f ( x ) = \frac { x - 4 } { 4 } , \quad g ( x ) = 4 x + 4f(x)=4x−4​,g(x)=4x+4

Determine Whether the Given Functions Are Inverses of Each Other $f ( x ) = \frac { x - 4 } { 4 } , \quad g ( x ) = 4 x + 4$