Suppose that f: X→Y and g: Y→Z are functions. Please teach me how to write the convers and inverse of the following statement. And what is a counter example of the converse? If both f and g are one-to-one, then g(f(x)): X→Z is one to one.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
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Suppose that f: X→Y and g: Y→Z are functions. Please teach me how to write the convers and inverse of the following statement. And what is a counter example of the converse?

If both f and g are one-to-one, then g(f(x)): X→Z is one to one.

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