Decide whether or not the functions are inverses of each other.Use the definition of inverses to determine whether f and g are inverses.
-$$f ( x ) = 9 x ^ { 2 } + 9 , x \geq 0 ; \quad g ( x ) = \sqrt { \frac { x - 9 } { 9 } } , x \geq 9$$
A) No
B) Yes

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)), substituting g(x) into f gives f(√((x-9)/9)) = 9((x-9)/9) + 9 = x. For g(f(x)), substituting f(x) into g gives g(9x^2 + 9) = √((9x^2 + 9 - 9)/9) = √(x^2) = x, since x ≥ 0. Both conditions are satisfied, so f and g are inverses.

Decide Whether or Not the Functions Are Inverses of Each f(x)=9x2+9,x≥0;g(x)=x−99,x≥9f ( x ) = 9 x ^ { 2 } + 9 , x \geq 0 ; \quad g ( x ) = \sqrt { \frac { x - 9 } { 9 } } , x \geq 9f(x)=9x2+9,x≥0;g(x)=9x−9​​,x≥9

Decide Whether or Not the Functions Are Inverses of Each $f ( x ) = 9 x ^ { 2 } + 9 , x \geq 0 ; \quad g ( x ) = \sqrt { \frac { x - 9 } { 9 } } , x \geq 9$