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  3. let f : x → y and g : y → z be funct

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

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Advance Math

Let f : X → Y and g : Y → Z be functions. We can define thecomposition of f and g to be the function g◦ f : X → Z for whichthe image of each x ∈ X is g(f(x)). That is, plug x into f, thenplug theresultinto g (justlikecompositioninalgebraandcalculus). (a)If f and g arebothinjective,must g◦ f beinjective? Explain. (b) Iff 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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