Let A = R - {1} and define f: A→A by f(x) = (a) Find fo f(x). (b) Find fofo f(x). (c) Find f-¹(x). (d) Determine if f is bijective. x-1 for all x € A.
Let A = R - {1} and define f: A→A by f(x) = (a) Find fo f(x). (b) Find fofo f(x). (c) Find f-¹(x). (d) Determine if f is bijective. x-1 for all x € 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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Transcribed Image Text:Let \( A = \mathbb{R} - \{1\} \) and define \( f : A \to A \) by \( f(x) = \frac{x}{x-1} \) for all \( x \in A \).
(a) Find \( f \circ f(x) \).
(b) Find \( f \circ f \circ f(x) \).
(c) Find \( f^{-1}(x) \).
(d) Determine if \( f \) is bijective.
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