# Chapter 1 - Test - Page 305: 14

$f(x)$, domain $(-\infty, \infty)$, range $(-\infty,\infty)$ $f^{-1}$, domain $(-\infty, \infty)$, range $(-\infty,\infty)$

#### Work Step by Step

Step 1. Find the inverse of the first function as $g(x)=f^{-1}=(x+1)^{1/3}$ Step 2. For function $f(x)=x^3-1$, shown as the red curve in the figure, we can identify its domain as $(-\infty, \infty)$ and its range as $(-\infty,\infty)$ Step 3. For function $g(x)=f^{-1}=(x+1)^{1/3}$, shown as the blue curve in the figure, we can identify its domain as $(-\infty, \infty)$ and its range as $(-\infty,\infty)$

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