Instructions: Use the chain rule and properties of inverse functions. Question: Let f be a one-to-one, differentiable function with inverse f¹. Prove that: Requirements: • Use the identity f(f¯¹(x))· = d 1 dx -f¹(x) = f'(f-¹(x)) • Differentiate both sides using the chain rule. Provide justification for all differentiability assumptions. • Discuss when the formula may fail.

Instructions: Use the chain rule and properties of inverse functions. Question: Let f be a one-to-one, differentiable function with inverse f¹. Prove that: Requirements: • Use the identity f(f¯¹(x))· = d 1 dx -f¹(x) = f'(f-¹(x)) • Differentiate both sides using the chain rule. Provide justification for all differentiability assumptions. • Discuss when the formula may fail.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.5: Rational Functions

Problem 47E

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