Associated Topics || Dr. Math Home || Search Dr. Math

### Unraveling an Inverse Function

```
Date: 11/30/2001 at 00:58:00
From: Trevor Lyons
Subject: Inverse functions

I had this question on a test and got it wrong.

f(x) = -5x-2
----
-x+1

the answer is y = -x-2
----
-x+5  restriction cannot equal 5.

I have no clue how to work this out, and would really like to know
how to do it.

Thanks,
Trevor
```

```
Date: 11/30/2001 at 01:18:18
From: Doctor Schwa
Subject: Re: Inverse functions

In other words, y = (-5x - 2) / (-x + 1).

Then the inverse function is what "undoes" that; in other words, the
opposite, turning y into x instead of x into y.

So, the common way to find it is to switch x and y with each other in
order to start "unraveling" the function:

x = (-5y - 2) / (-y + 1).

Now to solve for y, multiply both sides by (-y + 1) to get

x (-y + 1) = -5y - 2

Distribute,

-xy + x = -5y - 2

Collect all the y's on one side, and the rest of the terms on the
other:

-xy + 5y = -x - 2

Factor out the y,

(-x + 5)y = -x - 2

and finally divide,

y = (-x - 2) / (-x + 5)

so

-1       -x - 2
f  (x) = --------
-x + 5

The restriction on x is that the denominator -x + 5 cannot equal zero,
so x cannot equal 5. In other words, the domain of the inverse is all
real numbers except 5.

I hope that helps clear things up. If not, feel free to write back.

- Doctor Schwa, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Basic Algebra
High School Functions

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search