Give a formal proof or a counterexample to each of the follo

Give a formal proof or a counterexample to each of the following:

a) f(x) = x^2 is not a bijection because bijection means both injection and surjection.

But f(x) = x^2 is not an injection as x belongs to Z.

f(2) = 4

f(-2) = 4

This is against the definition f(x) = f(y), x = y, because f(2) = f(-2) but 2 -2

b)f(x) = x^2 -10x + 21 = (x-7)(x-3)

at x= 7, f(x) = 0

at x= 3, f(x) = 0

f(3) = f(7), but 37.

This is against the definition f(x) = f(y), x = y.

So, it is not injection.

c) h(x) = 3x+5 is a surjection because for the given function, for every x in Q, there exists a y in Q.