Decide whether or not the functions are inverses of each other.
-$f ( x ) = \sqrt { x + 7 }$, domain $[ - 7 , \infty ) ; g ( x ) = x ^ { 2 } + 7$, domain $( - \infty , \infty )$
A) Yes
B) No

Question

Quizplus · Accepted Answer

The functions are not inverses of each other because the composition $ f(g(x)) $ does not equal $ x $ for all $ x $ in the domain of $ g $, and $ g(f(x)) $ does not equal $ x $ for all $ x $ in the domain of $ f $. Specifically, $ f(g(x)) = \sqrt{x^2 + 7 + 7} \neq x $ and $ g(f(x)) = (\sqrt{x + 7})^2 + 7 = x + 7 + 7 \neq x $.

Decide Whether or Not the Functions Are Inverses of Each f(x)=x+7f ( x ) = \sqrt { x + 7 }f(x)=x+7​

Decide Whether or Not the Functions Are Inverses of Each $f ( x ) = \sqrt { x + 7 }$