# Question #2f4ab

May 15, 2017

Answer: $f ' \left(x\right) = \sqrt{\frac{x}{4}}$

#### Explanation:

Find inverse of $f \left(x\right) = 4 {x}^{2}$

Note that $f \left(x\right)$ is same as $y$

So, $y = 4 {x}^{2}$

To find the inverse, we flip $x$ and $y$ in the original equation:
$x = 4 {y}^{2}$

Now, we can simply solve for $y$ as for a normal equation:
$\frac{x}{4} = {y}^{2}$
$y = \sqrt{\frac{x}{4}}$
or
$f ' \left(x\right) = \sqrt{\frac{x}{4}}$
since we use $f ' \left(x\right)$ to indicate inverse functions