Home
Class 12
MATHS
Letf(x)={{:(-1+sinK(1)pix",", "x is rati...

Let`f(x)={{:(-1+sinK_(1)pix",", "x is rational."), (1+cosK_(2)pix",", x):}`
If f(x) is a periodic function, then

A

either `K_(1),K_(2) in` rational or `K_(1),K_(2) in` irrational

B

`K_(1),K_(2) in " rational only "`

C

`K_(1),K_(2) in " irrational only "`

D

`K_(1),K_(2) in " irrational such that " K_(1)/K_(2)` is rational

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise For Session 1|5 Videos

  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise For Session 2|6 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

If f(x) = {{:("sin"(pix)/(2)",",x lt 1),([x]",",x ge 1):} , where [x] denotes the greatest integer function, then

If f(x) = {{:(1, "if x is rational"),(-1, "If x is irrational"):}} , then f : R to R is :

Let f (x) be a real vaued continuous function such that f (0) =1/2 and f(x+y) = f(x) f (4-y) + f(y) f (4-x ) AA x, y in R, then for some real a: a. f(x) is a periodic function b. f(x) is a constant function c. f(x)=1/2 d. f(x)=(cosx)/2

Let the function f : R rarr R f(x) = {:{(1,if x is a rational)(-1, if x is irrational):}} be many one into Then f(1/2) is equal to

Let F (x) = (f (x ))^(2) + (f' (x ))^(2), F (0) =6, whtere f (x) is a thrice differentiable function such that |f (x) || le 1 AA x in [-1, 1], then choose the correct statement (s)

Let f(x) = sqrt(1-sqrt(1-x^2) then f(x) is

Q. For every integer n, let a_(n) and b_(n) be real numbers. Let function f:R->R be given by a f(x)={{:(a_n+sin pix, for x in [2n,2n+1]), (b_n+cos pix, for x in (2n+1,2n)):} for all integers n.

If a function satisfies f(x+1)+f(x-1)=sqrt(2)f(x) , then period of f(x) can be

Let f'(x)=(192x^(3))/(2+sin^(4)pix) for all x epsilonR with f(1/2)=0 . If mle int_(1//2)^(1)f(x)dxleM , then the possible values of m and M are

ARIHANT MATHS-FUNCTIONS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Letf(x)={{:(-1+sinK(1)pix",", "x is rational."), (1+cosK(2)pix",", x):...

    Text Solution

    |

  2. If the function f(x)=x^(3)+e^(x//2)andg(x)=f^(-1)(x), then the value ...

    Text Solution

    |

  3. Let F(x) be an indefinite integral of sin^(2)x Statement-1: The fun...

    Text Solution

    |

  4. Find the range of values of t for which 2sint=(1-2x+5x^2)/(3x^2-2x-1)

    Text Solution

    |

  5. Let F(k)(x)=1/k (sin^(k)x+cos^(k)x), where x in R and k ge 1, then fin...

    Text Solution

    |

  6. Let f:R-R be defined as f(x) = x^4, then (a) f is one-one (b) f is man...

    Text Solution

    |

  7. Let f(x)=x^2a n dg(x)=sinx for all x in R Then the set of all x satis...

    Text Solution

    |

  8. Let f:(0,1)->R be defined by f(x)=(b-x)/(1-bx), where b is constant s...

    Text Solution

    |

  9. Let f be a real-valued function defined on the inverval (-1,1) such th...

    Text Solution

    |

  10. If X and Y are two non-empty sets where f: X->Y,is function is define...

    Text Solution

    |

  11. If f(x)={x, when x is rational and 0, when x is irrational g(x)={0, w...

    Text Solution

    |

  12. If f(x)=sinx+cosx, g(x)=x^(2)-1, then g(f(x)) is invertible in the do...

    Text Solution

    |

  13. The domain of definition of the function f(x)=sqrt(sin^(-1)(2x)+pi/6) ...

    Text Solution

    |

  14. The range of the function f(x)=(x^2+x+2)/(x^2+x+1),x in R , is (a) (...

    Text Solution

    |

  15. If f:[0,infty) rarr [0,infty) " and " f(x)=x/(1+x), then f is

    Text Solution

    |

  16. If f:R to R be defined by f(x) =2x+sinx for x in R, then check the na...

    Text Solution

    |

  17. Let E={1,2,3,4} and F={1,2}dot If N is the number of onto functions fr...

    Text Solution

    |

  18. Suppose f(x)=(x+1)^(2) " for " x ge -1. If g(x) is the function whos...

    Text Solution

    |

  19. If F :[1,oo)->[2,oo) is given by f(x)=x+1/x ,t h e n \ f^(-1)(x) equal...

    Text Solution

    |

  20. Let f(x)=(1+b^2)x^2+2b x+1 and let m(b) the minimum value of f(x)dot A...

    Text Solution

    |

  21. Find the domain of the following functions. f(x)=(log(2)(x+3))/((x^(...

    Text Solution

    |