Decide whether or not the functions are inverses of each other.
-$$f ( x ) = \sqrt { x + 3 } , x \geq - 3 ; g ( x ) = x ^ { 2 } + 3$$
A)Yes
B)No

Question

Quizplus · Accepted Answer

To determine if two functions are inverses of each other, we check if $f(g(x)) = x$ and $g(f(x)) = x$. Here, $f(g(x)) = f(x^2 + 3) = \sqrt{x^2 + 3 + 3} = \sqrt{x^2 + 6}$, which is not equal to $x$. Similarly, $g(f(x)) = g(\sqrt{x + 3}) = (\sqrt{x + 3})^2 + 3 = x + 3 + 3 = x + 6$, which is also not equal to $x$. Therefore, the functions are not inverses of each other.

Decide Whether or Not the Functions Are Inverses of Each f(x)=x+3,x≥−3;g(x)=x2+3f ( x ) = \sqrt { x + 3 } , x \geq - 3 ; g ( x ) = x ^ { 2 } + 3f(x)=x+3​,x≥−3;g(x)=x2+3

Decide Whether or Not the Functions Are Inverses of Each $f ( x ) = \sqrt { x + 3 } , x \geq - 3 ; g ( x ) = x ^ { 2 } + 3$