Let f : X → Y and g : Y → Z be functions. We can...

Let f : X → Y and g : Y → Z be functions. We can deﬁne the composition of f and g to be the function g◦ f : X → Z for which the image of each x ∈ X is g(f(x)). That is, plug x into f, then plug theresultinto g (justlikecompositioninalgebraandcalculus). (a) If f and g arebothinjective,must g◦ f beinjective? Explain. (b) If f and g arebothsurjective,must g◦ f besurjective? Explain. (c) Suppose g◦ f isinjective. What,ifanything,canyousayabout f and g? Explain. (d) Suppose g◦f issurjective. What,ifanything,canyousayabout f and g? Explain.

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Colby Messinger answered 2 years ago

3. Let F : X → Y and G: Y → Z be functions. i. If...

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Let f : X → Y and g : Y → Z be functions. We can...

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