# Given f(x)= x^3 +2x -1, how do you find 1/ [f^(-1)(2)]?

Oct 9, 2016

$\frac{1}{f} ^ \left(- 1\right) \left(2\right) = 1$

#### Explanation:

If $f \left(x\right) = 2$ then we have:

${x}^{3} + 2 x - 1 = 2$

and so:

$0 = {x}^{3} + 2 x - 3 = \left(x - 1\right) \left({x}^{2} + x + 3\right) = \left(x - 1\right) \left({\left(x + \frac{1}{2}\right)}^{2} + \frac{11}{4}\right)$

So the only Real root is $x = 1$ and we find:

$\frac{1}{f} ^ \left(- 1\right) \left(2\right) = \frac{1}{1} = 1$