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. (a) Let f: X→ Y and g: Y→ Z be functions. Show that go f: X→ Z is a function too. (b) If f: X→ Y and g: Y→ Z are one-to-one functions, is gof one-to-one? (c) If f: X→ Y and g: Y→ Z are functions and g of is one-to-one, must g be one- to-one? Prove or give a counterexample. (d) If f:X→Y and g: Y→ Z are functions and go f is onto, must g be onto? Prove or give a counterexample.

. (a) Let f: X→ Y and g: Y→ Z be functions. Show that go f: X→ Z is a function too. (b) If f: X→ Y and g: Y→ Z are one-to-one functions, is gof one-to-one? (c) If f: X→ Y and g: Y→ Z are functions and g of is one-to-one, must g be one- to-one? Prove or give a counterexample. (d) If f:X→Y and g: Y→ Z are functions and go f is onto, must g be onto? Prove or give a counterexample.

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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. (a) Let f:X → Y and g: Y→ Z be functions. Show that go f: X→ Z is a function too. (b) If f: X→ Y and g: Y→ Z are one-to-one functions, is g of one-to-one? (c) If f: X→ Y and g: Y→ Z are functions and g of is one-to-one, must g be one- to-one? Prove or give a counterexample. (d) If f:X→Y and g: Y→ Z are functions and go f is onto, must g be onto? Prove or give a counterexample.
Transcribed Image Text:. (a) Let f:X → Y and g: Y→ Z be functions. Show that go f: X→ Z is a function too. (b) If f: X→ Y and g: Y→ Z are one-to-one functions, is g of one-to-one? (c) If f: X→ Y and g: Y→ Z are functions and g of is one-to-one, must g be one- to-one? Prove or give a counterexample. (d) If f:X→Y and g: Y→ Z are functions and go f is onto, must g be onto? Prove or give a counterexample.
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