Firstly remember that an inverse may not always exist.
If it does, then I find the following method the simplest:
1. Rewrite the equation \(f(x)=5x^2-1\) as \(y=5x^2-1\)
2. Swap the x and y's to get: \(x=5y^2-1\)
3. Solve for y:
\(x=5y^2-1\)
\(x+1=5y^2\)
\(\frac{x+1}{5} = y^2\)
\(\sqrt{\frac{x+1}{5}} =y\)
\(\therefore y=\sqrt{\frac{x+1}{5}}\)
This last step represents the inverse function
