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

Question

asked Jul 20, 2023 143k views

1 Answer

Scottyaz · Answer 1 · 2023-07-25T06:59:14+0000

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

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.