If `f(x)` satisfies the relation `f(x)+f(x+4)=f(x+2)+f(x+6)` for all`x ,` then prove that `f(x)` is periodic and find its period.

If f(x+2a)=f(x-2a) ,then prove that f(x) is periodic

If f(x) satisfies the relation 2f(x)+(1-x)=x^(2) for all real x, then find f(x) .

If f (x) satisfies the relation 2 f(x ) + f(1-x) =x^2 for all real x, then f (x) is

If f(x+2a)=f(x-2a), then prove that f(x) is periodic.

If f: Rrarr[0,oo) is a function such that f(x-1)+f(x+1)=sqrt(3)f(x), then prove that f(x) is periodic and find its period.

If f:R rarr[0,oo) is a function such that f(x-1)+f(x+1)=sqrt(3)f(x), then prove that f(x) is periodic and find its period.

If f: Rrarr[0,oo) is a function such that f(x-1)+f(x+1)=sqrt(3)f(x), then prove that f(x) is periodic and find its period.

If f (x) satisfies the relation : 2 f(x) +f (1 -x) = x^2 for all real x, then f (x) is :

If a , b are two fixed positive integers such that f(a+x)=b+[b^3+1-3b^2f(x)+3b{f(x)}^2-{f(x)}^3]^(1/3) for all real x , then prove that f(x) is periodic and find its period.

If a , b are two fixed positive integers such that f(a+x)=b+[b^3+1-3b^2f(x)+3b{f(x)}^2-{f(x)}^3]^(1/3) for all real x , then prove that f(x) is periodic and find its period.