# Inverse functions

1. Dec 14, 2004

### aisha

Determine f(f-1(x)) and f-1(f(x)) of the following functions. What do you notice?

a.) f(x) = 7x-3
b.)f(x) = 2/3 x+2 (there were no brackets the x+2 is just beside the fraction)

Rule: If f(g(x)) = x and f(f(x)) = x, then f(x) and g(x) are inverse of each other.

This is my exercise question I dont understand what to do I get the rule but how am getting an answer of x? I have the solutions also, but I dont know what to do with the numbers am I solving for something? :uhh:

2. Dec 14, 2004

### learningphysics

Did you work out f(f-1(x)) and f-1(f(x))? Which numbers are you referring too?

3. Dec 14, 2004

### Gokul43201

Staff Emeritus
Correction : If f(g(x)) = x and g(f(x)) = x, then f(x) and g(x) are inverse of each other, or g = f^-1. That should give you the answer.

4. Dec 14, 2004

### aisha

I understand that but I dont know what to do? lol Omg I dont even know what to do with the numbers given. Show me please The solutions are both are inverses of each other.

5. Dec 14, 2004

### Skomatth

Well you have to find the inverse of f(x) first. Then show $$f(f^{-1}(x)) = x$$. Can you find an inverse? An inverse g(x) is the graph of f(x) reflected across the line y=x .

For example:

$$f(x) = 1/x + 5$$

Defined implicitly the inverse is therefore:

$$x= 1/y + 5$$

where

$$y= f^{-1}$$

solve for y to get the inverse defined explicitly:

$$y = \frac{1}{x-5}$$

6. Dec 14, 2004

### aisha

Yes I know how to find the inverse that much makes sense but what does the stuff in these brackets mean? f(f^(-1)(x))=x what do I do after I find the inverse? multiply f? by the inverse? Thats the part I dont get how to =x :uhh:

7. Dec 14, 2004

### Skomatth

$$f(f^{-1}(x)) = x$$
is a composite function . Do you know about these? BTW what math level are you in, what circumstances are you in? It seems like you have an awful lot of questions that could be answered by reading the textbook.

8. Dec 15, 2004

### learningphysics

Suppose you have two different functions:
f(x)=3x+1
g(x)=x^2+1

You get a composite function f(g(x)) by taking g(x) and plugging into f(x) where x is:
So f(g(x))=3(x^2+1)+1

And g(f(x))=(3x+1)^2+1

Now let's look at a function and its inverse:
f(x)=3x+1
f-1(x)=(x-1)/3

I form the composite of f(x) with f-1(x)
f(f-1(x))=3[(x-1)/3]+1=(x-1)+1=x

f-1(f(x))=[(3x+1)-1]/3=(3x)/3=x

So we find f(f-1(x))=f-1(f(x))=x

This is always true for any relation and its inverse. So you should notice the same thing in your exercise.

9. Dec 17, 2004

### aisha

WOW THANKS SOOOO MUCH what a great explanation and example!!! So easy to understand, Thankyou. :rofl: