Decide whether or not the functions are inverses of each other.
-$$f ( x ) = 7 x - 7 , g ( x ) = \frac { 1 } { 7 } x + 1$$
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 $g(f(x)) = x$. Substituting $g(x)$ into $f(x)$, we get $f(g(x)) = 7\left(\frac{1}{7}x + 1\right) - 7 = x + 7 - 7 = x$. Substituting $f(x)$ into $g(x)$, we get $g(f(x)) = \frac{1}{7}(7x - 7) + 1 = x - 1 + 1 = x$. 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)=7x−7,g(x)=17x+1f ( x ) = 7 x - 7 , g ( x ) = \frac { 1 } { 7 } x + 1f(x)=7x−7,g(x)=71​x+1

Decide Whether or Not the Functions Are Inverses of Each $f ( x ) = 7 x - 7 , g ( x ) = \frac { 1 } { 7 } x + 1$