Question #9099e

1 Answer
Mar 9, 2017

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! :)