Answer
$f(x)=3x-6$, domain $(-\infty,\infty)$, range $(-\infty,\infty)$;
$f^{-1}(x)=\frac{1}{3}x+2$, domain $(-\infty,\infty)$, range $(-\infty,\infty)$
Work Step by Step
1. Given $f(x)=3x-6$, we can identify it is one-to-one with domain $(-\infty,\infty)$ and range $(-\infty,\infty)$
2. Rewrite the function as $y=3x-6$
3. Exchange $x,y$ to get $x=3y-6$
4. Solve for $y$ to get $y=\frac{x+6}{3}=\frac{1}{3}x+2$
5. Replace $y$ with $f^{-1}(x)$ to get $f^{-1}(x)=\frac{1}{3}x+2$
6. For $f^{-1}(x)$, we can find its domain $(-\infty,\infty)$ and range $(-\infty,\infty)$
