Home
Class 12
MATHS
Let f(x) be a real valued periodic funct...

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

Text Solution

Verified by Experts

The correct Answer is:
f(x) is periodic with period 2p.
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise For Session 8|8 Videos

  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise For Session 9|10 Videos

  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise For Session 6|5 Videos

  • ESSENTIAL MATHEMATICAL TOOLS

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|3 Videos

  • GRAPHICAL TRANSFORMATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|10 Videos

Similar Questions

Explore conceptually related problems

Let f be a real valued function with domain R satisfying f(x+k)=1+[(2-5f(x)+10{f(x)}^(2)-10{f(x)}^(3)+5{f(x)}^(4)-{f(x)}^(5)]^(5) for all real x and some positive constant k ,then the period of the function f(x)

Let f be a real vlaued fuction with domain R such that f(x+1)+f(x-1)=sqrt(2)f(x) for all x in R , then ,

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

Let f be a real-valued function such that f(x)+2f((2002)/(x))=3x. Then find f(x)

Let f be a real valued periodic function defined for all real umbers x such that for some fixed a gt 0 , f(x+a)=(1)/(2)+sqrt(f(x)-{f(x)}^(2)) for all x . Then , the period of f(x) is

Let f(x) be a real valued function such that f(0)=1/2 and f(x+y)=f(x)f(a-y)+f(y)f(a-x), forall x,y in R , then for some real a,

Statement -1: If f(x + a)f(x-a) = - 1 for some positive constant 'a' and for all value of x in R, then f (x) is periodic function with period equal to 4a.Statement - 2 : If f(x+T) = f(x), AA x in R and for some positive constant T, then f(x) is periodic function with period equal to T.

If f(x) is a real valued function such that f(x + 6) - f(x + 3) + f(x) = 0, AA x in R , then period of f(x) is

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.

f(x) is a polynomial function, f: R rarr R, such that f(2x)=f'(x)f''(x). The value of f(3) is