Decide whether or not the functions are inverses of each other.Use the definition of inverses to determine whether f and g are inverses.
-$$f ( x ) = 2 x + 4 , \quad g ( x ) = \frac { 1 } { 2 } x - 2$$
A) Yes
B) $\mathrm { No }$

Question

Quizplus · Accepted Answer

To determine if $f$ and $g$ are inverses, we check if $f(g(x)) = x$ and $g(f(x)) = x$. For $f(g(x))$, substitute $g(x)$ into $f$, yielding $f\left(\frac{1}{2}x - 2\right) = 2\left(\frac{1}{2}x - 2\right) + 4 = x$. For $g(f(x))$, substitute $f(x)$ into $g$, yielding $g(2x + 4) = \frac{1}{2}(2x + 4) - 2 = x$. Since both compositions return $x$, $f$ and $g$ are inverses.

Decide Whether or Not the Functions Are Inverses of Each f(x)=2x+4,g(x)=12x−2f ( x ) = 2 x + 4 , \quad g ( x ) = \frac { 1 } { 2 } x - 2f(x)=2x+4,g(x)=21​x−2

Decide Whether or Not the Functions Are Inverses of Each $f ( x ) = 2 x + 4 , \quad g ( x ) = \frac { 1 } { 2 } x - 2$