Chapter 6.2, Problem 5CYU

To determine

To find: The inverse of the given function and the graph of given function and its inverse.

Answer to Problem 5CYU

The inverse of the given function is $y=\pm \sqrt{x+3}$ .

Explanation of Solution

Given:

The given function is $h\left(x\right)=x^2-3$

Calculation:

The inverse of a function is obtained by interchanging the variables and then finding the new value of the function.

Interchange the variables of the function,

  $\begin{array}{l}y=x^2-3\\ x=y^2-3\end{array}$

Solve for y .

  $y=\pm \sqrt{x+3}$

Therefore, the inverse of the given function is $y=\pm \sqrt{x+3}$ .

The plot of $h\left(x\right)=x^2-3$ is :

  

The plot of the inverse $y=\pm \sqrt{x+3}$ is