Define f: R – {0} → R – {7} by f(x) = 7+,Vx € R.Prove that f is one to one. Here R – {0} means all non-zero real numbers and R - {7} means all real numbers except 7.
Define f: R – {0} → R – {7} by f(x) = 7+,Vx € R.Prove that f is one to one. Here R – {0} means all non-zero real numbers and R - {7} means all real numbers except 7.
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:Define \( f: \mathbb{R} - \{0\} \to \mathbb{R} - \{7\} \) by \( f(x) = 7 + \frac{1}{x} \), \( \forall x \in \mathbb{R} \). Prove that \( f \) is one to one.
Here \( \mathbb{R} - \{0\} \) means all non-zero real numbers and \( \mathbb{R} - \{7\} \) means all real numbers except 7.
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