Question

2. Define a function f : Z → Z × Z by f(x) = (x 2...

2. Define a function f : Z → Z × Z by f(x) = (x 2 , −x).

(a) Find f(1), f(−7), and f(0).

(b) Is f injective (one-to-one)? If so, prove it; if not, disprove with a counterexample.

(c) Is f surjective (onto)? If so, prove it; if not, disprove with a counterexample.

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Answer #1

Let a function   by  

a)

  

b)   f is injective (one-to-one).

if     

Which implies   which implies f is injective

c) f is not surjective (onto)

for any    

If there there n such that

where 3 is not square

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