# If y =sqrt(x -1), what is the inverse?

Nov 22, 2016

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

#### Explanation:

The inverse is obtained by switching the $x$ and $y$ values.

$y = \sqrt{x - 1} \to {f}^{-} 1 \left(x\right) \to x = \sqrt{y - 1}$

Solve for $y$.

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

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

Hopefully this helps!