Decide whether or not the functions are inverses of each other.
-$$f ( x ) = ( x - 6 ) ^ { 2 } , x \geq 6 ; g ( x ) = \sqrt { x } + 6$$
A)Yes
B)No

Question

Quizplus · Accepted Answer

To determine if $f(x)$ and $g(x)$ are inverses of each other, we check if $g(f(x)) = x$ and $f(g(x)) = x$. Substituting $f(x) = (x - 6)^2$ into $g(x)$, we get $g(f(x)) = \sqrt{(x - 6)^2} + 6 = x$, because $x \geq 6$ ensures the square root yields $x - 6$. Similarly, substituting $g(x) = \sqrt{x} + 6$ into $f(x)$, we get $f(g(x)) = (\sqrt{x} + 6 - 6)^2 = x$. Since both compositions return $x$, $f(x)$ and $g(x)$ are indeed inverses of each other.

Decide Whether or Not the Functions Are Inverses of Each f(x)=(x−6)2,x≥6;g(x)=x+6f ( x ) = ( x - 6 ) ^ { 2 } , x \geq 6 ; g ( x ) = \sqrt { x } + 6f(x)=(x−6)2,x≥6;g(x)=x​+6

Decide Whether or Not the Functions Are Inverses of Each $f ( x ) = ( x - 6 ) ^ { 2 } , x \geq 6 ; g ( x ) = \sqrt { x } + 6$