5. Let f(x) = x³ +x – 1. It turns out that f(x) is an invertible function (you don't need to prove this) and its inverse is denoted as f-'(x). (a) By trial and error, find a value r such that f(x) = -3. (b) What is the value of f-1(-3)? (c) Calculate the value of (f-1)'(-3), the derivative of f-1 at x = -3. Note: f-1(x) and (f-1)'() are too difficult to find; you are not asked to find those functions. You are ONLY asked for the value of (f-1)'(-3).
5. Let f(x) = x³ +x – 1. It turns out that f(x) is an invertible function (you don't need to prove this) and its inverse is denoted as f-'(x). (a) By trial and error, find a value r such that f(x) = -3. (b) What is the value of f-1(-3)? (c) Calculate the value of (f-1)'(-3), the derivative of f-1 at x = -3. Note: f-1(x) and (f-1)'() are too difficult to find; you are not asked to find those functions. You are ONLY asked for the value of (f-1)'(-3).
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:5. Let f(x) = x³ +x – 1. It turns out that f(x) is an invertible function (you don't need to prove this) and its
inverse is denoted as f-(x).
(a) By trial and error, find a value x such that f(x) = -3.
(b) What is the value of f-1(-3)?
(c) Calculate the value of (f-1)'(-3), the derivative of f-1 at x = -3.
Note: f-1(x) and (f-1)'(x) are too difficult to find; you are not asked to find those functions. You are
ONLY asked for the value of (f-1)'(-3).
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