10. (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 go f is one-to-one, must g be to-one? Prove or give a counterexample. one- (d) If f:X→Y and g: Y→ Z are functions and g of is onto, must g be onto? Prove or give a counterexample.
10. (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 go f is one-to-one, must g be to-one? Prove or give a counterexample. one- (d) If f:X→Y and g: Y→ Z are functions and g of is onto, must g be onto? Prove or give a counterexample.
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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Transcribed Image Text:10.
(a) Let f: XY and g: Y→ Z be functions. Show that go f: X→ Z is a function too.
(b) If f: XY and g: Y→ Z are one-to-one functions, is g of one-to-one?
(c) If f: XY and g: Y→ Z are functions and g of is one-to-one, must g be
to-one? Prove or give a counterexample.
one-
(d) If f: XY and g: Y→ Z are functions and g of is onto, must g be onto?
Prove
or give a counterexample.
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