Help with inverse functions

• Sep 2nd 2012, 03:04 PM
vysero
Help with inverse functions
Here is my problem:

Find the inverse F^-1 of f(x)=x-4/1+3x

They give me a hint and the hint is *use the two step method. I am not sure where to start even.
• Sep 2nd 2012, 03:33 PM
Plato
Re: Help with inverse functions
Quote:

Originally Posted by vysero
Here is my problem:
Find the inverse F^-1 of f(x)=x-4/1+3x
They give me a hint and the hint is *use the two step method. I am not sure where to start even.

Solve $x=\frac{y-4}{1+3y}$ for $y$. Then $F^{-1}(x)=y.$
• Sep 2nd 2012, 04:21 PM
HallsofIvy
Re: Help with inverse functions
Any function can be thought of as a set of ordered pairs: {(x, y)}. The corresponding inverse function, if there is one, is the set {(y, x)}. That's why Plato swapped x and y in the given formula, Technically, once you have done that, you have the inverse function. But in order to show that this is a "function", you need to solve for y.

(If I were doing a problem that has, as a hint, "use the two step method", I would start by leafing back through the previous chapters to find out what the "two step method" was.)