if `a,b` are two positive numbers 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 peroidic and find its peroid?

if a,b are two positive numbers 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.

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.

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.

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

Find positive real numbers 'a' and 'b' such that f(x) =ax- bx^(3) has four extrema on [-1,1] at each of which |f(x)|=1

If f(x)=x^3+b x^2+c x+d and f(0),f(-1) are odd integers, prove that f(x)=0 cannot have all integral roots.

If f(x)=x+(1)/(x) , then prove that : {f(x)}^(3)=f(x^(3))+3*f((1)/(x))