Question

What is the inverse of the function f(x)= 2x+1

Answer 1

f'(x) =
`(x-1)/(2)`

Explanation:

Let y be equal to f(x).

This means that y = 2x+1.

Now rearrange for x:

2x = y -1

x =
`(y-1)/(2)`

If you now bring x back in place for y, this is the inverse of the function, so f'(x) is
`(x-1)/(2)`.

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) =
`(5-1)/(2)` = 4/2 = 2, so it is the inverse.