Find the inverse of each of the following bijections. а) и: Q — Q, u(x) = 3x – 2. - v(x) = . b) v: Q – {1} → Q – {2}, c) w: Z → Z, x-1 w(n) = n + 3.
Find the inverse of each of the following bijections. а) и: Q — Q, u(x) = 3x – 2. - v(x) = . b) v: Q – {1} → Q – {2}, c) w: Z → Z, x-1 w(n) = n + 3.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Transcribed Image Text:**5. Find the inverse of each of the following bijections.**
(a) \( u: \mathbb{Q} \to \mathbb{Q}, \quad u(x) = 3x - 2. \)
(b) \( v: \mathbb{Q} - \{1\} \to \mathbb{Q} - \{2\}, \quad v(x) = \frac{2x}{x-1}. \)
(c) \( w: \mathbb{Z} \to \mathbb{Z}, \quad w(n) = n + 3. \)
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