(a) Which of the following are functions? If f is not a function explain why. i. f :R →R with f(x) = ii. f : Z → Z with f(x) = 5 ii. f :R →R with f (x) = In(x) (b) Let f : R →Rand g : R +R with f (x) = x + 2 and g(x) = -x. Find gof, (go f)-', f-1 and g- (c) Let f : R' → R with f(x) = , where R' is the set of all real numbers different from 0. i. Determine whether or not f is a one to one function ii. Determine whether or not f is an onto function

(a) Which of the following are functions? If f is not a function explain why. i. f :R →R with f(x) = ii. f : Z → Z with f(x) = 5 ii. f :R →R with f (x) = In(x) (b) Let f : R →Rand g : R +R with f (x) = x + 2 and g(x) = -x. Find gof, (go f)-', f-1 and g- (c) Let f : R' → R with f(x) = , where R' is the set of all real numbers different from 0. i. Determine whether or not f is a one to one function ii. Determine whether or not f is an onto function

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

(a) Which of the following are functions? If f is not a function explain why.
i. f :R →R with f(x) =
ii. ƒ :Z → Z with f(x) =
iii. f :R → R with f(x) = ln(x)
(b) Let f : R → R and g : R → R with f(x) = x + 2 and g(x) = -x. Find
gof, (go f)-', f-' and g-
(c) Let f : R* → R with f(x) = , where R* is the set of all real numbers
different from 0.
i. Determine whether or not f is a one to one function
ii. Determine whether or not f is an onto function
(d) Given a function F : P({a,b,c}) → Z is defined by F(A) = |4| for all
A E P({a,b, c}).
i. Is Fa one-to-one function? Prove or give a counter-example.
ii. Is F an onto function? Prove or give a counter-example.
(e) Let f : A → B and g : B → C be functions. Prove that if go f is one-to-one
then f is also one-to-one.

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