# Question #92c0c

Apr 22, 2016

I am convinced I have answered this one before!

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

#### Explanation:

Given:$\text{ } f \left(x\right) = x + \frac{1}{2}$

Set this equal to y giving:

$\text{ } y = x + \frac{1}{2}$

Subtract $\frac{1}{2}$ from both sides

$\text{ } y - \frac{1}{2} = x + \frac{1}{2} - \frac{1}{2}$

$\text{ } y - \frac{1}{2} = x + 0$

Write as:

$x = y - \frac{1}{2}$
'~~~~~~~~~~~~~~~~~~~~~~~
Where there is a $x$ write $y$ and where there is a $y$ write $x$.

$\implies y = x - \frac{1}{2}$

Thus $\textcolor{b l u e}{{f}^{- 1} \left(x\right) \to y = x - \frac{1}{2}}$

This will be a reflection about $y = x$ of $f \left(x\right)$