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.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.5: The Kernel And Range Of A Linear Transformation

Problem 30EQ

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