Problem 7. Consider the funcrtion f : R - {1} → R - {1} given by x+1 x-1 f(x) = Show that f is its own inverse. I.e., (ƒ o f-¹)(x) = x and (f-1 o f)(x) = x for all x € R - {1}.
Problem 7. Consider the funcrtion f : R - {1} → R - {1} given by x+1 x-1 f(x) = Show that f is its own inverse. I.e., (ƒ o f-¹)(x) = x and (f-1 o f)(x) = x for all x € R - {1}.
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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![**Problem 7.** Consider the function \( f: \mathbb{R} - \{1\} \to \mathbb{R} - \{1\} \) given by
\[
f(x) = \frac{x+1}{x-1}
\]
Show that \( f \) is its own inverse. I.e., \( (f \circ f^{-1})(x) = x \) and \( (f^{-1} \circ f)(x) = x \) for all \( x \in \mathbb{R} - \{1\} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0df08f65-d573-4be5-901b-9fd2cfa38a4f%2Fe6511027-9a80-4964-85a6-55f604982308%2F9d837hl_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 7.** Consider the function \( f: \mathbb{R} - \{1\} \to \mathbb{R} - \{1\} \) given by
\[
f(x) = \frac{x+1}{x-1}
\]
Show that \( f \) is its own inverse. I.e., \( (f \circ f^{-1})(x) = x \) and \( (f^{-1} \circ f)(x) = x \) for all \( x \in \mathbb{R} - \{1\} \).
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