Let f : X → Y and g : Y → Z be functions. We can deï¬ne thecomposition of f and g to be the function gâ—¦ 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 gâ—¦ f beinjective? Explain. (b) Iff and g arebothsurjective,must gâ—¦ f besurjective? Explain. (c)Suppose gâ—¦ f isinjective. What,ifanything,canyousayabout f and g?Explain. (d) Suppose gâ—¦f issurjective.What,ifanything,canyousayabout f and g? Explain.
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