Decide whether or not the functions are inverses of each other.
-$$f ( x ) = ( x - 2 ) ^ { 2 } , x \geq 2 ; g ( x ) = \sqrt { x } + 2$$
A) Yes
B) No

Question

Quizplus · Accepted Answer

To determine if $f(x)$ and $g(x)$ are inverses of each other, we can check if $f(g(x)) = x$ and $g(f(x)) = x$. For $f(x) = (x - 2)^2, x \geq 2$ and $g(x) = \sqrt{x} + 2$, we find that $f(g(x)) = (\sqrt{x} + 2 - 2)^2 = x$ and $g(f(x)) = \sqrt{(x - 2)^2} + 2 = x$, given the domain restrictions. Therefore, $f$ and $g$ are inverses of each other.

Decide Whether or Not the Functions Are Inverses of Each f(x)=(x−2)2,x≥2;g(x)=x+2f ( x ) = ( x - 2 ) ^ { 2 } , x \geq 2 ; g ( x ) = \sqrt { x } + 2f(x)=(x−2)2,x≥2;g(x)=x​+2

Decide Whether or Not the Functions Are Inverses of Each $f ( x ) = ( x - 2 ) ^ { 2 } , x \geq 2 ; g ( x ) = \sqrt { x } + 2$