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11. (a) Define f: RR by f(x) = x² - 4 for all x € R. Explain why the inverse of the function f is not a function. (b) Let R* = {x = R | x>0} and let T = {y = R | y ≥ -4}. Define F:R* → T by F(x) = x² - 4 for all x € R*. Explain why the inverse of the function F is a function and find a formula for F-1 (y), where y € T.

11. (a) Define f: RR by f(x) = x² - 4 for all x € R. Explain why the inverse of the function f is not a function. (b) Let R* = {x = R | x>0} and let T = {y = R | y ≥ -4}. Define F:R* → T by F(x) = x² - 4 for all x € R*. Explain why the inverse of the function F is a function and find a formula for F-1 (y), where y € T.

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter8: Functions
Section8.1: Concept Of A Function
Problem 100PS
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11. (a) Define f: RR by f(x) = x² - 4 for all x € R. Explain why the inverse of the function f is not a function. (b) Let R* = {x = R | x>0} and let T = {y = R | y ≥ -4}. Define F:R* → T by F(x) = x² - 4 for all x € R*. Explain why the inverse of the function F is a function and find a formula for F-1 (y), where y € T.
Transcribed Image Text:11. (a) Define f: RR by f(x) = x² - 4 for all x € R. Explain why the inverse of the function f is not a function. (b) Let R* = {x = R | x>0} and let T = {y = R | y ≥ -4}. Define F:R* → T by F(x) = x² - 4 for all x € R*. Explain why the inverse of the function F is a function and find a formula for F-1 (y), where y € T.
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