Question

Graph the function y=2x²+4, and then graph its inverse as a reflection over the line y = x. Is the inverse of the graph also a function?

Answer 1

The inverse of the graph of y = 2x² + 4 is also a function

The inverse is y = √[(x - 4)/2]

How to determine if the inverse is also a function

From the question, we have the following parameters that can be used in our computation:

y = 2x² + 4

Swap the variables x and y

So, we have

x = 2y² + 4

Make y the subject of the formula

So, we have

2y² = x - 4

This gives

y² = (x - 4)/2

Take the square root of both sides

y = √[(x - 4)/2]

This means that the inverse of y = 2x² + 4 is y = √[(x - 4)/2]

The graphs are attached and we can see that the inverse is a function