Prove that every number b can be written b = f(a)

[andmcg]

Homework Statement

I am trying to learn how to write proofs and this proof seems weird...

Suppose f o g = I. Prove that every number b can be written b = f(a) for some number a.

Homework Equations

f(g(x))=I(x)=x

The Attempt at a Solution

Here's my stab at it.
Let g(x)=a
f(g(x))=f(a)=x
Let x=b
Then b=f(a)

This really doesn't seem sufficient to me however. What I'm trying to say is that I can choose x to equal any number b. With the application of g upon x=b I get some number a. Then with the application of f upon a i get back the number I wanted, namely b.

 

[Dick]

Put x=b, sure. Then you have f(g(b))=b. So put a=g(b). Then f(a)=b, right? You are maybe just thinking about this too hard.