1. Let f (0, ∞)→ R be the function with f(x) = |1 ln x]. Sketch the graph of y = f(x). Give a brief justification (one sentence each) why f is not injective and why f is not surjective. Come up with a subset A of R of your choice such that the function g: A → R with g(x) = 1 In x is injective. No justification needed. Come up with a subset B of R of your choice such that the function h: (0, ∞) → B with h(x) = 1- ln x is surjective. No justification needed.
1. Let f (0, ∞)→ R be the function with f(x) = |1 ln x]. Sketch the graph of y = f(x). Give a brief justification (one sentence each) why f is not injective and why f is not surjective. Come up with a subset A of R of your choice such that the function g: A → R with g(x) = 1 In x is injective. No justification needed. Come up with a subset B of R of your choice such that the function h: (0, ∞) → B with h(x) = 1- ln x is surjective. No justification needed.
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:1. Let f (0,00)→ R be the function with f(x)= |1 - Inx. Sketch the graph of
y = f(x). Give a brief justification (one sentence each) why f is not injective and why
f is not surjective.
Come up with a subset A of R of your choice such that the function g: A → R with
g(x) = 1 In x is injective. No justification needed.
Come up with a subset B of R of your choice such that the function h: (0, ∞) → B
with h(x) = 1 In x is surjective. No justification needed.
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