Question #3877e

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Answer 1 · 2016-04-16T20:50:12

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

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

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

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

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

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

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

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

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