Problem 2: For the following statements, answer true or false. If the statement is true, provide a short reason. If the statement is false, provide a counterexample (or explain why). (a) If a function is injective, then it admits a unique left inverse. (b) Let f be injective. If f'(x) > 1, then the derivative of f-1 is less than 1. (c) For all r E [-1, 1], 2 arccos(x) = arccos(2x² – 1). (d) The function 2 sinh(x) cosh² (x) is bijective. (e) Suppose f and g are two (continuous) functions defined on [2a, 2b] (with b > a) such that f(x) > g(x) everywhere. Then one can compute the area bounded by these functions via: ra-b I g(x + a+b) – f(x+ a+b) dx. 6-a
Problem 2: For the following statements, answer true or false. If the statement is true, provide a short reason. If the statement is false, provide a counterexample (or explain why). (a) If a function is injective, then it admits a unique left inverse. (b) Let f be injective. If f'(x) > 1, then the derivative of f-1 is less than 1. (c) For all r E [-1, 1], 2 arccos(x) = arccos(2x² – 1). (d) The function 2 sinh(x) cosh² (x) is bijective. (e) Suppose f and g are two (continuous) functions defined on [2a, 2b] (with b > a) such that f(x) > g(x) everywhere. Then one can compute the area bounded by these functions via: ra-b I g(x + a+b) – f(x+ a+b) dx. 6-a
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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