which two functions are inverses of each other?\n○ (f(x)=x,g(x)= - x)\n○ (f(x)=2x,g(x)=-\frac{1}{2}x)\n○…

Answer:

C. $f(x) = 4x, g(x)=\frac{1}{4}x$

Explanation:

Step1: Recall inverse - function property

Two functions $f(x)$ and $g(x)$ are inverses if $f(g(x))=x$ and $g(f(x))=x$.

Step2: Check option A

For $f(x)=x$ and $g(x)= - x$, $f(g(x))=f(-x)=-x\neq x$.

Step3: Check option B

For $f(x)=2x$ and $g(x)=-\frac{1}{2}x$, $f(g(x))=f(-\frac{1}{2}x)=2\times(-\frac{1}{2}x)=-x\neq x$.

Step4: Check option C

For $f(x)=4x$ and $g(x)=\frac{1}{4}x$, $f(g(x))=f(\frac{1}{4}x)=4\times\frac{1}{4}x = x$ and $g(f(x))=g(4x)=\frac{1}{4}\times4x=x$.

Step5: Check option D

For $f(x)=-8x$ and $g(x)=8x$, $f(g(x))=f(8x)=-8\times8x=-64x\neq x$.