Determine whether the given functions are inverses of each other.
-$$f ( x ) = \sqrt { x } , x \geq 0 , \quad g ( x ) = \frac { 1 } { \sqrt { x } } , x \geq 0$$
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 $g(f(x)) = x$. For $f(x) = \sqrt{x}$ and $g(x) = \frac{1}{\sqrt{x}}$, $f(g(x)) = \sqrt{\frac{1}{\sqrt{x}}} = \frac{1}{\sqrt[4]{x}}$ and $g(f(x)) = \frac{1}{\sqrt{\sqrt{x}}} = \frac{1}{\sqrt[4]{x}}$, neither of which simplifies to $x$. Therefore, they are not inverses of each other.

Determine Whether the Given Functions Are Inverses of Each Other f(x)=x,x≥0,g(x)=1x,x≥0f ( x ) = \sqrt { x } , x \geq 0 , \quad g ( x ) = \frac { 1 } { \sqrt { x } } , x \geq 0f(x)=x​,x≥0,g(x)=x​1​,x≥0

Determine Whether the Given Functions Are Inverses of Each Other $f ( x ) = \sqrt { x } , x \geq 0 , \quad g ( x ) = \frac { 1 } { \sqrt { x } } , x \geq 0$