Question

已知 f(x) 是定义在实数集R上的偶函数,且f(x)+f(x+2)=2.若x∈[0,2)时,f (x)=2-x,则f(7.5)=?求过程

Answer 1

f(7.5)= 2 - f(5.5) = 2 - (2 - f(3.5)) = f(3.5) = 2 - f(1.5) = 2 - (2-1.5) = 1.5

Answer 2

f(7.5)=f(5+5.5)
=2-f(5.5)
=2-f(2+3.5)
=2-[2-f(3.5)]
=f(3.5)
=f(2+1.5)
=2-f(1.5)
=2-(2-1.5)
=1.5

Answer 3

f(7.5)=f(5+5.5)
=2-f(5.5)
=2-f(2+3.5)
=2-[2-f(3.5)]
=f(3.5)
=f(2+1.5)
=2-f(1.5)
=2-(2-1.5)
=1.5
=f(5+5.5)
=2-f(5.5)
=2-f(2+3.5)
=2-[2-f(3.5)]
=f(3.5)
=f(2+1.5)
=2-f(1.5)
=2-(2-1.5)
=1.5