Question

Solving y in terms of x I want to determine the inverse of the function by interchanging the variables

Answer 1

To find the inverse first replace every x with a y and replace every y with an x:

$\begin{gathered} y=4x^2 \\ \text{First step} \\ x=4y^2 \end{gathered}$

Now, solve for y:

$\begin{gathered} \text{Divide both sides by 4:} \\ \frac{x}{4}=\frac{4y^2}{4} \\ \text{Simplify} \\ \frac{x}{4}=y^2 \\ \text{Apply square root to both sides} \\ \sqrt[]{\frac{x}{4}}=\sqrt[]{y^2} \\ \text{Simplify and apply the properties of square roots} \\ \frac{\sqrt[]{x}}{\sqrt[]{4}}=y \\ y=\frac{\sqrt[]{x}}{2} \end{gathered}$

The inverse of the given function is y=square root(x)/2