# Thread: Composite Functions! Help! :|

1. ## Composite Functions! Help! :|

My teacher assigned some work from the textbook and I'm not really understanding it. He told us to think of composite functions as a "machine," where there are inputs and outputs of each function.

The question I'm having trouble with is:

If f(x) = 1/(1-x) and g(x) = 1-x, determine:

a. g(f(x)) and b. f(g(x)).

Are there any specific methods to doing these problems? The exemplars aren't really helping very much. :|

2. ## Here's how you do it...

a) g(f(x))

This is g(1/1-x) because you sub in f(x) into the g function.

With me so far???

Since g(x)=1-x, sub 1/1-x in for the x in 1-x

the function now is 1-(1/1-x)
which is (1-x)-1
which is -x
I think that's it...
Hope that helps!

3. The textbook says the answer to a is equal to x/(x-1), while b is 1/x.

Hmm...

4. $\displaystyle f(x)=\frac{1}{1-x}$ and $\displaystyle g(x)=1-x$

then for a...
$\displaystyle g(f(x))= 1-f(x) = 1-\frac{1}{1-x}=\frac{-x}{1-x}=\frac{x}{x-1}$
and for b...
$\displaystyle f(g(x))=\frac{1}{1-g(x)}=\frac{1}{1-(1-x)}=\frac{1}{x}=\frac{1}{x}$

I hope this helps...