true or false? PROVE YOUR ANSWER b) If f :N→N and g :N→N are functions such that f is not onto but  fg is onto, then g is onto. The claim is of answer:                           prove of answer

Determine if the statements below true or false. Justify your answer (provide a reason, no need for a formal proof Statement attached  Thank you

4. Let f : R+ x Z → R+ be the function defined by f(x,n) = x", where R+ is the set of positive real numbers and Z is the set of integers. (a) Is f one-to-one? Give a proof for your answer. (b) Is f onto? Give a proof for your answer. (c) Determine f-1({1}).

Let f be a function from Z×Z to Z×Z (that is, f maps pairs of integers to pairs of integers) given by f (x, y) = (x + y, xy). Is f one-to-one? onto? Prove or give a counterexample