MathDB

Function Problem

Source: 1992 National High School Mathematics League, Exam One, Problem 6

February 26, 2020

function

Problem Statement

f(x)

is a function defined on

\mathbb{R}

, satisfying:

f(10+x)=f(10-x),f(20-x)=-f(20+x)

. Then,

f(x)

\text{(A)}

even function, but not periodic function

\text{(B)}

even function, and periodic function

\text{(C)}

odd function, but not periodic function

\text{(D)}

odd function, and periodic function