If f(x)=2 x-x^2 , then what is the value of f(x+2)+f(x-2) when x=0 ?

Step-by-step solution

aligned & f(x)=2 x-x^2 & f(x+2)+f(x-2) aligned aligned & =2(x+2)-(x+2)^2+2(x-2)-(x-2)^2 & =4+4 x-x^2-4-4 x-x^2-4+4 x-4 aligned =8 x-2 x^2-8 When x=0 , then, f(x+2)+f(x-2)=-8