Home
Class 12
MATHS
If f : R -> R be a function such that f(...

If `f : R -> R` be a function such that `f(x) = { x|x| -4; x in Q, x|x| - sqrt3; x !in Q` then f(x) is

A

one-one, onto

B

many one, onto

C

one-one, into

D

many one, into

Text Solution

Verified by Experts

The correct Answer is:
D
NA
Promotional Banner

Topper's Solved these Questions

  • RELATION, FUNCTION & ITF

    RESONANCE|Exercise INTEGER_TYPE|21 Videos

  • RELATION, FUNCTION & ITF

    RESONANCE|Exercise MCQ_TYPE|31 Videos

  • RELATION, FUNCTION & ITF

    RESONANCE|Exercise MATCH THE COLUMN|5 Videos

  • NUMBER THEORY

    RESONANCE|Exercise Exercise -2 (PART - II)|4 Videos

  • SEQUENCE & SERIES

    RESONANCE|Exercise EXERCISE -2 (PART-II : PREVIOUSLY ASKED QUESTION OF RMO)|3 Videos

Similar Questions

Explore conceptually related problems

If f:R rarr R be a function such that f(x)={x|x|-4;x in Q,x|x|-sqrt(3);x!in Q then f(x) is

Let f :R to R be a function such that f(x) = x^3 + x^2 f' (0) + xf'' (2) , x in R Then f(1) equals:

If f:R rarr R-{3} be a function such that f(x+1)=(f(x)-5)/(f(x)-3)AA x in R, then

Function f:R rarr R,f(x)=x|x| is

If f: R to [0,∞) be a function such that f(x -1) + f(x + 1) = sqrt3(f(x)) then prove that f(x + 12) = f(x) .

If f : R to R be a function such that f(x)=x^(3)+x^(2)+3x +sinx, then discuss the nature of the function.

Given a function f' such that f(x)=5x+4 , x in R ,if g:R rarr R is the inverse of f' ' then

function f: R to R: f(x) =x^(3) is

RESONANCE-RELATION, FUNCTION & ITF-SCQ_TYPE
  1. If domain of f(x) is(-oo,0], then domain of f(6{x}^2-5(x)+ 1) is (wher...

    Text Solution

    |

  2. Let f: (e, oo) -> R be defined by f(x) =ln(ln(In x)), then

    Text Solution

    |

  3. If f(x) =2 [x]+ cos x, then f: R ->R is: (where [ ] denotes greatest ...

    Text Solution

    |

  4. If f : R -> R be a function such that f(x) = { x|x| -4; x in Q, x|x| -...

    Text Solution

    |

  5. f(x) = |x-1|, f: R^+->R, g(x) = e^x, g:[-1,oo)->R. If the function fog...

    Text Solution

    |

  6. Let f:(2,4)->(1,3) where f(x) = x-[x/2] (where [.] denotes the greates...

    Text Solution

    |

  7. The mapping f: R->R given by f(x) = x^3 + ax^2 + bx + c is bijection i...

    Text Solution

    |

  8. If the function f:[1,oo)to[1,oo) is defined by f(x)=2^(x(x-1)) then f^...

    Text Solution

    |

  9. Let f:N->N, where f(x)=x+(-1)^(x-1), then the inverse of f is.

    Text Solution

    |

  10. tan(pi/4+1/2cos^-1x)+tan(pi/4-1/2cos^-1x), x!=0 is equal to

    Text Solution

    |

  11. The value of cot^(-1){(sqrt(1-sinx)+sqrt(1+sinx))/(sqrt(1-sinx)-sqrt(1...

    Text Solution

    |

  12. The domain of the function f (x) = sin^(-1)((1+x^3)/(2x^(3/2)))+sqrt(s...

    Text Solution

    |

  13. A function g(x) satisfies the following conditions (i) Domain of g i...

    Text Solution

    |

  14. The complete solution set of the inequality [cot^(-1)x]^2-6[cot^(-1)x]...

    Text Solution

    |

  15. sin^-1(sin 5)> x^2-4 x holds if

    Text Solution

    |

  16. If sin^(- 1)(x-(x^2)/2+(x^3)/4-.....)+cos^(- 1)(x^2-(x^4)/2+(x^6)/4-....

    Text Solution

    |

  17. if cot^(-1)[sqrt(cosalpha)]-tan^(-1)[sqrt(cosalpha)]=x then sinx is eq...

    Text Solution

    |

  18. The equation sin^(-1) x = 2 sin^(-1) alpha has a solution

    Text Solution

    |

  19. If f(x)=cot^-1 x ; R^+ -> (0,pi/2) and g(x)=2x-x^2 ; R-> R . Then t...

    Text Solution

    |

  20. Q. Given the functions f(x)=e^(cos^-1(sin(x+pi/3))), g(x)=cosec^-1((4-...

    Text Solution

    |