Chapter 10.4, Problem 23E

To determine

To find the inverse of the function.

Answer to Problem 23E

  $f^{-1}\left(x\right)=\frac{\sqrt{x}}{2}$

Explanation of Solution

Given information: $f(x)=4x^2,x\ge 0$

Formula Used: Inverse Relation

Calculation:

If a relation contains the point $\left(x,y\right)$ then the Inverse Relation contains the point $\left(y,x\right)$ because the inverse relation interchange the x and y coordinates.

  $f(x)=4x^2,x\ge 0$

As,

  $y=f(x)$

So,

  $y=4x^2$

Now,

  $x^2=\frac{y}{4}$

So, square root both sides.

  $\sqrt{x^2}=\sqrt{\frac{y}{4}}$

Now, simplify

  $x=\frac{\sqrt{y}}{2}$

Hence,

  $f^{-1}\left(x\right)=\frac{\sqrt{x}}{2}$