Chapter 3, Problem 31T

Solution

To graph the function $y=-6\sqrt[3]{x}$ and state the domain and range.

The graph of the function is,

  

Domain: $\left(-\infty ,\infty \right)$

Range: $\left(-\infty ,\infty \right)$

Given information:

The function $y=-6\sqrt[3]{x}$ .

Concept used:

• The graph of the function $y=f\left(x\right)$ and its inverse $f^{-1}\left(x\right)$ are symmetric to the line $y=x$ .
• For any point $\left(a,b\right)$ on the graph of $f\left(x\right)$ , the corresponding point on the graph of inverse function $f^{-1}\left(x\right)$ is $\left(b,a\right)$ .
• If a function is one-to-one, then it has an inverse.

Calculation:

The graph of the function $y=-6\sqrt[3]{x}$ is shown below,

  

Since the domain of a function $y=f\left(x\right)$ is the set of x -values, the domain of the given function includes all real numbers, that is, the domain is $\left(-\infty ,\infty \right)$ .

Since the range of a function $y=f\left(x\right)$ is the set of y -values, the range of the given function includes all real numbers, that is, the domain is $\left(-\infty ,\infty \right)$ .