select the correct answer. which function is the inverse of $f(x)=x^{2}-16$ if the domain of $f(x)$ is…

select the correct answer. which function is the inverse of $f(x)=x^{2}-16$ if the domain of $f(x)$ is $xgeq0$?\na. $f^{-1}(x)=sqrt{x + 16}$\nb. $f^{-1}(x)=sqrt{x}+4$\nc. $f^{-1}(x)=sqrt{x - 16}$\nd. $f^{-1}(x)=sqrt{x}-4$

select the correct answer. which function is the inverse of $f(x)=x^{2}-16$ if the domain of $f(x)$ is $xgeq0$?\na. $f^{-1}(x)=sqrt{x + 16}$\nb. $f^{-1}(x)=sqrt{x}+4$\nc. $f^{-1}(x)=sqrt{x - 16}$\nd. $f^{-1}(x)=sqrt{x}-4$

Answer

Answer:

A. $f^{-1}(x)=\sqrt{x + 16}$

Explanation:

Step1: Set $y = f(x)$

$y=x^{2}-16$

Step2: Swap $x$ and $y$

$x=y^{2}-16$

Step3: Solve for $y$

$y^{2}=x + 16$. Since $x\geq0$ for $f(x)$, and the inverse function should be well - defined, $y=\sqrt{x + 16}$ (we take the positive square root because the domain of $f(x)$ is non - negative, so the range of the inverse is non - negative).