Decide whether or not the functions are inverses of each other.
-$$f ( x ) = 9 x - 9 , g ( x ) = \frac { 1 } { 9 } x + 1$$
A) Yes
B) No

Question

Quizplus · Accepted Answer

To determine if $f(x)$ and $g(x)$ are inverses, we check if $f(g(x)) = x$ and $g(f(x)) = x$. For $f(g(x))$, substitute $g(x)$ into $f(x)$: $f(g(x)) = 9(\frac{1}{9}x + 1) - 9 = x + 9 - 9 = x$. For $g(f(x))$, substitute $f(x)$ into $g(x)$: $g(f(x)) = \frac{1}{9}(9x - 9) + 1 = x - 1 + 1 = x$. 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)=9x−9,g(x)=19x+1f ( x ) = 9 x - 9 , g ( x ) = \frac { 1 } { 9 } x + 1f(x)=9x−9,g(x)=91​x+1

Decide Whether or Not the Functions Are Inverses of Each $f ( x ) = 9 x - 9 , g ( x ) = \frac { 1 } { 9 } x + 1$