Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Discrete Math. Just abc.
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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