f: R→ R and g: Z → Z by the rules f(x) g(n) = n² for all n € Z. (i) Is f onto? Prove or give a counterexample. (ii) Is g onto? Prove or give a counterexample. 3r5 for all r ER and

Consider the Boolean function F(x, y, z) = x(y + xz + z). a. Use a table to express the function. b. Find the sum of products expansion of the function F(x, y, z) using rules. If you can't do this use a table for partial credit.

(b) Let z = x + iy = re?". Find |z| and z² first in terms of x and y and then in terms of r and 0. Under what circumstances does |z| = z2?

Find the condition of c such that x² + 2y² +3z² + c(xy + yz) > 0 for all x, y, z & R with x² + y² + z² # 0.