Question

Question #9099e

Answer 1

`f(x)^-1=x^2/8+7/2`

This can also be written as one fraction:

`f(x)^-1 = (x^2 +28)/8`

Explanation:

Rules
When finding the inverse, `f^(-1)(x)`, the easiest method is to switch the variables `x` and `y`. So `y=f(x)` is now `x=f(y)`.
Afterwards, you need to isolate `y` again to get the proper form of the inverse.

Application
`f(x)=y=2(2x-7)^(1/2)" "` Applying the "switch" ...

`f(y)=x=2(2y-7)^(1/2)`

Solving for `y` ...

`x=2\sqrt{2y-7}`

`1/2x=\sqrt{2y-7}`

`(1/2x)^2=2y-7`

`1/4x^2+7=2y`

`1/2(1/4x^2+7)=y`

`1/8x^2+7/2=y`

Confused? Feel free to drop a comment and tell me where you're still not understanding things! :)