Chapter 6.2, Problem 51E

To determine

To determine the inverse of the function and then graph the function and its inverse

Answer to Problem 51E

The inverse of the function is $f^{-1}\left(x\right)={\left(x+2\right)}^{1/3}$

Explanation of Solution

Given information:

Consider the given information,

  $y=x^3-2$

Calculation:

Use graphing calculator to graph given the function,

  

The sketched graph is given for the function and its inverse of $y=x^3-2$

  $y=x^3-2$

Interchange the variables,

  $x=y^3-2$

Now, solve for $y$

  $y={\left(x+2\right)}^{1/3}$

Solving for $y$ and replace with $f^{-1}\left(x\right)$

Therefore, the inverse of the function is $f^{-1}\left(x\right)={\left(x+2\right)}^{1/3}$