# If F (x)=x^2-1 then find f inverse?

Apr 25, 2018

${f}^{- 1} \left(x\right) = \pm \sqrt{x + 1}$

#### Explanation:

Let $y = f \left(x\right) .$ Then,

$y = {x}^{2} - 1$

To determine the inverse function, switch the places of $x$ and $y$, and subsequently solve for $y :$

$x = {y}^{2} - 1$

${y}^{2} = x + 1$

$y = \pm \sqrt{x + 1}$

Since this is the inverse, $y = {f}^{- 1} \left(x\right)$:

${f}^{- 1} \left(x\right) = \pm \sqrt{x + 1}$