# Functions : Onto and One-to-one, Bijections and Function Composition 'f o g'

Please help with the following problems on graphs and functions. Provide step by step calculations.

1. Assuming A,B not equal to no solution, define m1:AxB->A and m2:AxB-> as follows: m1(x,y)=x and m2(x,y)=y. If f:

A->B, show that

a) f onto=>m2 |f is onto

b)f one-to-one=>m2 f is one-to-one

2. Assuming f: A->B and g: B->C are bijections, show that (g o f)^-1 = f^-1 o g^-1

3. Find a bijection from A to B when

a) A=[-2,3] and B=[5,14]

b) A=(0,infinity)and B=(-infinity, infinity)

c) A=Natural numbers and B={3,6,9,12,...}

https://brainmass.com/math/graphs-and-functions/functions-onto-one-to-one-bijections-and-functions-40592

#### Solution Preview

1. Proof:

(a) f is onto, then for any y in B, we can find x in A, such that f(x)=y. Then we have

m2(x,f(x))=f(x)=y. So m2 f is onto.

(b) f is one-to-one, then if ...

#### Solution Summary

This posting involves a problem about graphs and functions. Onto and One-to-one, Bijections and Function Composition are investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question. Step by step calculations are given for each problem.