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10.11. Let C = {x € R : x ≥ 1} and D = R+. For each function f defined below, determine f(C), f f'(D) and f¹({1}). (a) f: R → R is defined by f(x)=x². (b) f: R+ → R is defined by f(x) = In.x. (c) f: R → R is defined by f(x) = e.

10.11. Let C = {x € R : x ≥ 1} and D = R+. For each function f defined below, determine f(C), f f'(D) and f¹({1}). (a) f: R → R is defined by f(x)=x². (b) f: R+ → R is defined by f(x) = In.x. (c) f: R → R is defined by f(x) = e.

Advanced Engineering Mathematics
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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Discrete Math. Just abc.
**Exercise 10.11** Let \( C = \{x \in \mathbb{R} : x \geq 1\} \) and \( D = \mathbb{R}^+ \). For each function \( f \) defined below, determine \( f(C) \), \( f^{-1}(D) \), and \( f^{-1}(\{1\}) \). (a) \( f : \mathbb{R} \rightarrow \mathbb{R} \) is defined by \( f(x) = x^2 \). (b) \( f : \mathbb{R}^+ \rightarrow \mathbb{R} \) is defined by \( f(x) = \ln x \). (c) \( f : \mathbb{R} \rightarrow \mathbb{R} \) is defined by \( f(x) = e^x \). (d) \( f : \mathbb{R} \rightarrow \mathbb{R} \) is defined by \( f(x) = \sin x \). (e) \( f : \mathbb{R} \rightarrow \mathbb{R} \) is defined by \( f(x) = 2x - x^2 \).
Transcribed Image Text:**Exercise 10.11** Let \( C = \{x \in \mathbb{R} : x \geq 1\} \) and \( D = \mathbb{R}^+ \). For each function \( f \) defined below, determine \( f(C) \), \( f^{-1}(D) \), and \( f^{-1}(\{1\}) \). (a) \( f : \mathbb{R} \rightarrow \mathbb{R} \) is defined by \( f(x) = x^2 \). (b) \( f : \mathbb{R}^+ \rightarrow \mathbb{R} \) is defined by \( f(x) = \ln x \). (c) \( f : \mathbb{R} \rightarrow \mathbb{R} \) is defined by \( f(x) = e^x \). (d) \( f : \mathbb{R} \rightarrow \mathbb{R} \) is defined by \( f(x) = \sin x \). (e) \( f : \mathbb{R} \rightarrow \mathbb{R} \) is defined by \( f(x) = 2x - x^2 \).
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