# Question #3877e

Apr 16, 2016

Assumption:
The question is - find ${f}^{- 1} \left(x\right) \text{ given that } f \left(x\right) = x + \frac{1}{2}$

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

#### Explanation:

Write as: $y = x + \frac{1}{2}$

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

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

Write as: $x = y - \frac{1}{2}$ ....................(1)

In equation (1) where there is a $x$ write $y$ and where there is a $y$ write $x$ giving:

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

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What this process does is that it reflects the function about the line $y = x$