China Mathematical Competition

Question

The function f(x) = x1-2^x - x2 is ( ). (A) an even but not odd function (B) an odd but not even function (C) a both even and odd function (D) a neither even nor odd function

Accepted Answer

It is easy to see that the domain of f(x) is (-, 0) (0, +). When x (-, 0) (0, +), we have aligned f(-x) &= -x1-2^-x - x2 &= -x 2^x2^x - 1 + x2 &= x1-2^x - x + x2 &= x1-2^x - x2 = f(x). aligned Therefore, f(x) is an even function, and obviously not an odd function. Answer: A.