f'(x) = [tex]\frac{x-1}{2}[/tex]
Let y be equal to f(x).
This means that y = 2x+1.
Now rearrange for x:
2x = y -1
x = [tex]\frac{y-1}{2}[/tex]
If you now bring x back in place for y, this is the inverse of the function, so f'(x) is [tex]\frac{x-1}{2}[/tex].
This can be checked by testing a value for x.
For example, if x is 2, then f(x) is 2(2) + 1, so 5.
If you put 5 into the inverse function, you should get 2 back.
f'(x) = [tex]\frac{5-1}{2}[/tex] = 4/2 = 2, so it is the inverse.
