Prove the following statement. If f: R→ R is onto and c is any nonzero real number, then (c f) is also onto. Proof: Suppose f: R→ R is onto and c is any nonzero real number. Given any real number z in the ---Select--- ✓ of f, we must show that there is a real number in the -Select--- ✓ of f, say x, such that (c f)(x) = z. Let x be such that f(x) = and since ---Select--- ✓ this is a real number. So, since f is ---Select--- ✓, ✗ is in the domain of f. Now (c. f)(x) = = C • = Z. f(x) by definition of composition because f(x) = Thus, (c f) is onto [as was to be shown].