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If f:X→Y is a function and A⊆X, then define f(A) ={y∈Y:f(a) =y for some a∈A}. (a)...

If f:X→Y is a function and A⊆X, then define

f(A) ={y∈Y:f(a) =y for some a∈A}.

(a) If f:R→R is defined by f(x) =x^2, then find f({1,3,5}).

(b) If g:R→R is defined by g(x) = 2x+ 1, then find g(N).

(c) Suppose f:X→Y is a function. Prove that for all B, C⊆X,f(B∩C)⊆f(B)∩f(C). Then DISPROVE that for all B, C⊆X,f(B∩C) =f(B)∩f(C).

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