Question

Find the inverse of y = 5x^2 - 4

Answer 1

We need to find the inverse of the following function:

y = 5x² - 4

This can be easily done by changing places of x and y variables like this:

x = 5y² - 4

Now we have to solve for y. I'm going to rewrite the equation:

5y² - 4 = x

Okay, we're good to go. Add 4 on both sides:

5y² = x + 4

Divide by 5 both sides:

`y^(2)=(x)/(5)+(4)/(5)`

Sum the fractions on the right side:

`y^(2)=(x+4)/(5)`

Take the square root on both sides:

`y=\pm\sqrt[]{(x+4)/(5)}`

And that's our inverse function.