Please do part g. Please show step by step and explain (b) Suppose f: A → B and g: B → C. Show that if gof is one-to-one,then f is one-to-one.(c) Suppose f: A → B and g: B → C. Show that if g of is onto, then g isonto.(d) Give an example of functions f: A → B and g: B → C, such that gofis onto, but f is not onto.(e) Suppose f: A → B and g: B → C. Show that if g of is onto, and g isone-to-one, then ƒ is onto.(f) Suppose f: A → B and g: B → C. Show that if f is onto and gof is1-1, then g is 1-1.(g) Define f: [0, 0) →R by f(x) = x. Find a function g: R → R such thatgof is one-to-one, but g is not one-to-one.(h) Suppose f and g are functions from A to A. If f(a) = a for every a E A,then what are f og and go f?

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Answered: Define f : [0, 0) →R by f(x) = x. Find…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.2: Mappings

Problem 10E: For each of the following parts, give an example of a mapping from E to E that satisfies the given...

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Define f : [0, 0) →R by f(x) = x. Find a function g: R → R such that gof is one-to-one, but g is not one-to-one.