If is a function

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

f(x)

is a function

f:\mathbb{R}\to\mathbb{R}

, we say

f(x)

has property I. I. If

f(f(x))=x

for all real numbers

x

. II. If

f(-f(x))=-x

for all real numbers

x

. How many linear functions have both property I and II? (1) 0 (2) 2 (3) 3 (4) Infinite