- #1

- 5

- 0

## 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.