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:
[tex]y^{2}=\frac{x}{5}+\frac{4}{5}[/tex]Sum the fractions on the right side:
[tex]y^{2}=\frac{x+4}{5}[/tex]Take the square root on both sides:
[tex]y=\pm\sqrt[]{\frac{x+4}{5}}[/tex]And that's our inverse function.
