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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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