Home
Class 12
MATHS
f:RrarrR" defined by "f(x)=(1)/(2)x|x|+c...

`f:RrarrR" defined by "f(x)=(1)/(2)x|x|+cos+1` is

A

one-one and onto

B

one-one and into

C

many-one and onto

D

many-one and into

Text Solution

Verified by Experts

The correct Answer is:
A
Clearly `f(x)rarroo` when `x rarroo`
and `f(x)rarr-oo` when `x rarr-oo`
`therefore" Range is R as f(x) os continuous"`.
Also for `x ge f'(x)=|x|-sin x ge 0`
`therefore" f(x) is increasing"`
`therefore" f(x) is one-one."`
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    CENGAGE|Exercise Multiple Correct Answers Type|10 Videos

  • FUNCTIONS

    CENGAGE|Exercise Comprehension Type|7 Videos

  • EQUATION OF PLANE AND ITS APPLICATIONS -II

    CENGAGE|Exercise DPP 3.4|18 Videos

  • GETTING STARTED WITH GRAPHS

    CENGAGE|Exercise Exercise|18 Videos

Similar Questions

Explore conceptually related problems

If f:RrarrR is defined by f(x)=|x-2|+|x+2| for x epsilon R ,then lim_(xrarr2^-)f(x) is :

Show that f: RvecR defined by f(x)=(x-1)(x-2)(x-3) is surjective but not injective.

Let f: RrarrR be defined by f(x)=(e^x-e^(-x))//2dot Is f(x) invertible? If so, find is inverse.

Let f:""RrarrR be defined by f(x)""= {(k-2x , if xle-1),( 2x+3, if x gt-1):} . If f has a local minimum at x""=""1 , then a possible value of k is (1) 0 (2) -1/2 (3) -1 (4) 1

F : R to R defined by f (x) = (1)/(2x^2 +5) the range of F is

Let f:RtoR be defined by f(x)=x/(1+x^2),x inR . Then the range of f is

The function f : RR to RR is defined by f(x) = ((x^(2)+cos x)(1+x^(4)))/((x-sinx )(2x-x^(3)))+e^(-|x|) is

Which of the following functions has inverse function? a) f: ZrarrZ defined by f(x)=x+2 b) f: ZrarrZ defined by f(x)=2x c) f: ZrarrZ defined byy f(x)=x d) f: ZrarrZ defined by f(x)=|x|

CENGAGE-FUNCTIONS-Question Bank
  1. f:RrarrR" defined by "f(x)=(1)/(2)x|x|+cos+1 is

    Text Solution

    |

  2. If there are four distinct real numbers satisfying thẻ equation |x^2-4...

    Text Solution

    |

  3. Let f: R rarr R be a polynomial function satisfying f(f(x) -2 y)=2 x-3...

    Text Solution

    |

  4. Let P(x)=x^4+a x^3+b x^2+c x+d be a polynomial such that P(1)=1, P(2)=...

    Text Solution

    |

  5. A function f(x) is such that f(x)=0 has 8 distinct real roots and f(4+...

    Text Solution

    |

  6. The number of integral values of x satisfying the equation sgn([15/(1+...

    Text Solution

    |

  7. Let f(x)=(1-c x)/(1-c^2) . If f(x) gt 0 for évery x greater than zero....

    Text Solution

    |

  8. Let g:[-2,2] rarr R, where g(x)=x^(2015)+sgn(x)+[(x^2+1)/p] be an odd ...

    Text Solution

    |

  9. If f(x)=|x+2|+|2 x-p|+|x-2| attains its minimum value in the interval ...

    Text Solution

    |

  10. Let the function f: R rarr R be defined as f(x)=min .(x+2,4-2 x, 1+4 x...

    Text Solution

    |

  11. Let f: R rarr R be defined as f(x)=2 x^3+7 x-5 and g(x)=f^-1(x). If g^...

    Text Solution

    |

  12. If f(x)= 3 sqrt((9)/(log2 (3-2x) - 1) then the value of ' a ' which sa...

    Text Solution

    |

  13. Consider the function f(x)=sqrt(2-x)+sqrt(1+x). If d denotes the numb...

    Text Solution

    |

  14. If f(x, y)=(max (x, y))^(min (x, y)) and g(x, y)=max (x, y) -min (x, y...

    Text Solution

    |

  15. The number of solution of the equation e^(2 x) + e^x+e^-(2 x)+ e^(-x...

    Text Solution

    |

  16. Suppose f(x)=a x+ba n dg(x)=b x+a ,w h e r eaa n db are positive integ...

    Text Solution

    |

  17. Let f:R->R be a continuous function such that|f(x)-f(y)|>=|x-y| for a...

    Text Solution

    |

  18. Let the equation (a-1) x^2=x(2 b+3) be satisfied by three distinct val...

    Text Solution

    |

  19. f(x) = (2x^(2) + 3)/(5), for oo lt x le 1 = 6 -5x, for 1 lt x lt 3 ...

    Text Solution

    |

  20. Let f(x)=x/(1-x) and ' a ' be a real number. If x0=a, x1=f(x0) , x2=f(...

    Text Solution

    |

  21. If the largest positive value of the function defined as f(x)=sqrt(8 x...

    Text Solution

    |