Given the function f(x)=[3x+3(-x)]2,thenf(x+y)+f(x-y)=?
f(x)+f(y)
f(x)f(y)
12f(x)×f(y)
Explanation for the correct option::
Let
⇒f(x)=3x+3-x2⇒f(x+y)+f(x–y)=[3x+y+3-x-y]2+[3x-y+3-x+y]2=123x+3-x2×[3y+3-y]2
⇒f(x+y)+f(x–y)=(12)f(x)×f(y)
Hence, option(D) is correct.