if $f(x)=3x$ and $g(x)=\frac{1}{3}x$, which expression could be used to verify that $g(x)$ is the inverse of…

if $f(x)=3x$ and $g(x)=\frac{1}{3}x$, which expression could be used to verify that $g(x)$ is the inverse of $f(x)$?\n$3x(\frac{x}{3})$\n$(\frac{1}{3}x)(3x)$\n$\frac{1}{3}(3x)$\n$\frac{1}{3}(\frac{1}{3}x)$

if $f(x)=3x$ and $g(x)=\frac{1}{3}x$, which expression could be used to verify that $g(x)$ is the inverse of $f(x)$?\n$3x(\frac{x}{3})$\n$(\frac{1}{3}x)(3x)$\n$\frac{1}{3}(3x)$\n$\frac{1}{3}(\frac{1}{3}x)$

Answer

Answer:

A. $3x\left(\frac{x}{3}\right)$

Explanation:

Step1: Recall inverse - function property

For two functions $f(x)$ and $g(x)$ to be inverses of each other, $f(g(x))=x$ and $g(f(x)) = x$. Here $f(x)=3x$ and $g(x)=\frac{1}{3}x$. Then $f(g(x))=3\times\left(\frac{1}{3}x\right)=x$ and $g(f(x))=\frac{1}{3}(3x)=x$. The expression $3x\left(\frac{1}{3}x\right)$ (equivalent to $3\times\left(\frac{1}{3}x\right)$ when considering the order of operations) can be used to verify the inverse - relationship.