# G(f(x)) Im so lost.

1. Aug 18, 2011

### Deagonx

1. The problem statement, all variables and given/known data

g(f(x))
g(x) = 3/x+1
f(x)= 3x+2

2. Relevant equations

?

3. The attempt at a solution

Ive had none I dont even know how to attempt this problem.

2. Aug 18, 2011

### dynamicsolo

When you see a composite function, say, g( f(x) ) , that is saying that we will substitute the function f(x) everywhere that 'x' appears in the expression for g(x) . In your problem, this will mean that if g(x) = 3/x+1 ,

by the way, is this $$\frac{3}{x+1} or \frac{3}{x} + 1$$ (I will assume the first -- if you don't use TeX, be sure to use parentheses)

g( f(x) ) = 3 / [ f(x) + 1 ] = 3 / [ ( 3x + 2 ) + 1 ] ,

and make any necessary algebraic simplifications from there.

3. Aug 18, 2011

### GreenPrint

every were you see x in g(x) plug in f(x)

4. Aug 18, 2011

### I like Serena

Welcome to PF, Deagonx!

Try it like this:
g(f(x))
g(u) = 3/u+1
u = f(x) = 3x+2

5. Aug 18, 2011

### Ray Vickson

Maybe you know whether g(x) = 3/(x+1) or g(x) = (3/x) + 1, but nobody else does. Which one do you mean? (If I read it according to *standard rules*, it means the second form.)

RGV

6. Aug 19, 2011

### Deagonx

They way that I did it was as followed:

If f(x) = 3x + 2. and the equation is g(f(x)) then isn't it really just g(3x+2)

In which case, I came to 3/(3x+2) + 1 which I then simplified to x + 2.5 Which I think is wrong.

7. Aug 19, 2011

### dynamicsolo

This part is correct.

So $$f( g(x) ) = \frac{3}{(3x+2) + 1 } = \frac{3}{3x + 3} .$$ What would that simplify to?

8. Aug 19, 2011

### Deagonx

x + 1?

9. Aug 19, 2011

### dynamicsolo

This is a ratio: what can be done in the numerator and denominator? (Remember, the 3x + 3 is in the denominator.)

10. Aug 19, 2011

### Mentallic

And remember, if the original expression is equal to your new expression, whatever value of x you choose (granted you don't divide by zero), you should be able to plug it into both expressions and the same answer will come out!

11. Aug 19, 2011

### uart

The first part was correct, but the simplification was wrong.

To simplify that expression first put everything on a common denominator.

$$\frac{3}{3x+2} + 1 = \frac{3}{3x+2} + \frac{3x+2}{3x+2}$$

Then simplify it from there.

12. Aug 19, 2011

### dynamicsolo

Evidently, everyone still hasn't settled on what g(x) is. So at least we'll have both possible versions...

By the way, in this version,
$$f( g(x) ) = \frac{3}{(3x+2) + 1 } = \frac{3}{3x + 3} ,$$

you are dividing 3 by ( 3x + 3 ) , not ( 3x + 3 ) by 3 : that's why this version isn't x + 1 .

13. Aug 19, 2011

### uart

Yes it's difficult when the OP wont clarify that, even after being prompted a few times.

But without any other clarification I think we really have to go with what the OP is typing, whether or not that is really what he/she is actually trying to ask.