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^(2)f(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 positive numbers such that f(a+x)=b+[b^(3)+1-3b^(2)f(x)+3b{f(x)}^(2)-{f(x)}^(3)]^((1)/(3)) for all real x, then prove that f(x) is peroidic and find its peroid?

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: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(a-x)=f(a+x) " and " f(b-x)=f(b+x) for all real x, where a, b (a gt b gt 0) are constants, then prove that f(x) is a periodic function.

Let f(x) be a real valued periodic function with domain R such that f(x+p)=1+[2-3f(x)+3(f(x))^(2)-(f(x))^(3)]^(1//3) hold good for all x in R and some positive constant p, then the periodic of f(x) is

Let f: R to R be a periodic function such that f(T+x)=1" " where T is a +[1-3f(x)+3(f(x))^(2) -(f(x))^(3)]^(1/3) fixed positive number, then period of f(x) is

If f(x) satisfies the equation |[f(x-3),f(x+4),f((x+1)(x-2)-(x-1)^(2))],[5,4,-5],[5,6,15]|=0 for all real x then (A) f(x) is not periodic (B) f(x) is periodic and is of period 1 (C) f(x) is periodic and is of period 7 (D) f(x) is an odd function

Let f(x) be periodic and k be a positive real number such that f(x+k)+f(x)=0 for all x in R. Prove that f(x) is periodic with period 2k .

A function f is such that f(x+1)=f(x)+f(1)+1 for all real values of x . Find f(0) If it is given that f(1)=1, find f(2),f(3) and f(-1) .