Decide whether or not the functions are inverses of each other.
-$$f ( x ) = 5 x + 25 , g ( x ) = \frac { 1 } { 5 } x - 5$$
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 $g(f(x)) = x$. Substituting $g(x)$ into $f(x)$, $f(g(x)) = 5\left(\frac{1}{5}x - 5\right) + 25 = x - 25 + 25 = x$. Substituting $f(x)$ into $g(x)$, $g(f(x)) = \frac{1}{5}(5x + 25) - 5 = x + 5 - 5 = x$. 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)=5x+25,g(x)=15x−5f ( x ) = 5 x + 25 , g ( x ) = \frac { 1 } { 5 } x - 5f(x)=5x+25,g(x)=51​x−5

Decide Whether or Not the Functions Are Inverses of Each $f ( x ) = 5 x + 25 , g ( x ) = \frac { 1 } { 5 } x - 5$