Question

Find the inverse of f(x)=5x^2-3

Answer 1

Answer is below in picture.

Answer 2

`\large\boxed{y=\pm\sqrt{(x+3)/(5)}}`

To find the inverse, swap the
`y` (or
`f(x)` in this case) and the
`x`, then solve for
`y`.

`\begin{aligned}y&=5x^2-3\\x&=5y^2-3\\x+3&=5y^2-3+3\\x+3&=5y^2\\(x+3)/(5)&=(5y^2)/(5)\\(x+3)/(5)&=y^2\\\pm\sqrt{(x+3)/(5)}&=√(y^2)\\\pm\sqrt{(x+3)/(5)}&=y\end{aligned}`