If f(x) = (x+2)/2 , then what is f–1(x) ?

Question

anonymous · Answer

2x-2

jamesj · Answer

The easiest way to find the inverse function is to set
$$ x = f(y) $$
and then solve for y.

That works because if
$$ x = f(y) $$
then
$$ y = f^{-1}(x) $$

With your problem,
$$ f(x) = \frac{x+2}{2} $$

so if we start with x = f(y), we have

$$ x = \frac{y+2}{2} $$

Now solve that equation for y.

anonymous · Answer

$$f ^{-1}(x) = 2x-2$$

jamesj · Answer

@melissa, did what I wrote make sense?

jamesj · Answer

@amir and @yamaka.  Here on OpenStudy, we try to avoid just giving answers because it nearly always doesn't help the person asking the question to learn.  

So it's much better to explain how to get to an answer, than just giving it.  Or if you do give an answer, explain how you derived it.

jamesj · Answer

So, for the record if
$$ x = \frac{y+2}{2} $$
then
$$ 2x = y + 2 $$
hence
$$ y = 2x - 2 $$