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4. (a) Show that the function defined by f(x)=2x: (x+2) is one to one and onto from its domain to its range, Find the inverse f.

4. (a) Show that the function defined by f(x)=2x: (x+2) is one to one and onto from its domain to its range, Find the inverse f.

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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(x+2) is one to one and onto 4. (a) Show that the function defined by f(x) = from its domain to its range, Find the inverse f. 2x-3 (b) Define a function F:F: R XR → R XR as follows: For all (x, y) = R XR, F(x, y) = (x + y,x-y). Show that F is one to one and onto, and find its inverse F-1. (c) Show that the function f: R → R, by f(x) = x² is neither not one-to-one nor onto.
Transcribed Image Text:(x+2) is one to one and onto 4. (a) Show that the function defined by f(x) = from its domain to its range, Find the inverse f. 2x-3 (b) Define a function F:F: R XR → R XR as follows: For all (x, y) = R XR, F(x, y) = (x + y,x-y). Show that F is one to one and onto, and find its inverse F-1. (c) Show that the function f: R → R, by f(x) = x² is neither not one-to-one nor onto.
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