Prove that the function f : Z4 → Z12 given by f(T) = [3x] is well defined. x +1 Let f(x) = and g(x) = x? +1. x +2' i. Find fog, gof. What are the domains and ranges of these functions? ii. Determine if ƒ and g are one to one or onto. iii. Determine if fog or gof are one to one or onto.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 42E
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7. Q7; Functions
(a) Prove that the function f : Z4 → Z12 given by f(T) = [3x] is well
defined.
x +1
and g(x)
x +2
(b) Let f(x) =
= x2 + 1.
i. Find fo g, gof. What are the domains and ranges of these
functions?
ii. Determie if f and g are one to one or onto.
iii. Determine if f og or g of are one to one or onto.
Transcribed Image Text:7. Q7; Functions (a) Prove that the function f : Z4 → Z12 given by f(T) = [3x] is well defined. x +1 and g(x) x +2 (b) Let f(x) = = x2 + 1. i. Find fo g, gof. What are the domains and ranges of these functions? ii. Determie if f and g are one to one or onto. iii. Determine if f og or g of are one to one or onto.
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