jmc

Question

The function f(x) satisfies f(x + y) = f(x) f(y)for all real numbers x and y. Find all possible values of f(0). Enter all the possible values, separated by commas.

Accepted Answer

Setting x = y = 0, we get f(0) = f(0)^2,so f(0) = 0 or f(0) = 1. The constant functions f(x) = 0 and f(x) = 1 show that both 0,1 are possible values of f(x).