Assignment:
Let n be a natural number, and let f(x) = x^n for all x are members of R.
1) If n is even, then f is strictly increasing hence one-to-one, on [0,infinity) and f([0,infinity)) = [0,infinity).
2) If n is odd, then f is strictly increasing, hence one-to-one, on R and f(R) = R.
"This needs to be a proof by induction, proving the fact that f is strictly increasing. The proof needs to look at the values of n, not x"
Provide complete and step by step solution for the question and show calculations and use formulas.