Home
Class 12
MATHS
If f:R->R where f(x) = ax + cosx is an...

If `f:R->R` where `f(x) = ax + cosx` is an invertible function, then `(a).(-2, -1]uu [1,2)`; `(b).[-1,1]`; `(c).(-oo, -1]uu [1,oo)`; `(d).(-oo, -2]uu [2,oo)`.

A

`(-2, -1]uu [1,2)`

B

`[-1,1]`

C

`(-oo, -1]uu [1,oo)`

D

`(-oo, -2]uu [2,oo)`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • FUNCTION

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise ONE OR MORE THAN ONE ANSWE IS/ARE CORRECT|23 Videos
  • FUNCTION

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise COMPREHENSION TYPE PROBLEMS|13 Videos
  • ELLIPSE

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise-4 : Subjective Type Problems|2 Videos
  • HYPERBOLA

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise-4 : Subjective Type Problems|3 Videos

Similar Questions

Explore conceptually related problems

For x^2-(a+3)|x|-4=0 to have real solutions, the range of a is a) (-oo,-7]uu[1,oo) b) (-3,oo) c) (-oo,-7] d) [1,oo)

Range of f(x) =1/(1-2cosx) is (1) [1/3,1] (2) [-1,1/3] (3) (-oo,-1]uu[1/3,oo) (4) [-1/3,1]

If f(x)={x^3,if x^2 =1 then f(x) is differentiable at (a) (-oo,oo)-{1} (b) (-oo,oo)-{1,-1} (c) (-oo,oo)-{1,-1,0} (d) (-oo,oo)-{-1}

For x^2-(a+3)|x|+4=0 to have real solutions, the range of a is a. (-oo,-7]uu[1,oo) b. (-3,oo) c. (-oo,-7) d. [1,oo)

If |x-1|>5, then a. x in (-4,6) b. x in [-4,6] c. x in (-oo,-4)uu(6,oo) d. x in (-oo,-4)uu[6,oo)

If |x+2|lt=9 then x in (-7, 11) b. x in [-11 ,7] c. x in (-oo,7)uu(11 ,oo) d. x in (-oo,-7)uu[11 ,oo)

The domain of the function f(x)=(sin^(-1)(3-x))/(I n(|x|-2)i s (a) [2,4] (b) (2,3)uu(3,4] (c) (0,1)uu(1,oo) (d) (-oo,-3)uu(2,oo)

For x^2-(a+3)|x|=4=0 to have real solutions, the range of a is a (-oo,-7]uu[1,oo) b (-3,oo) c (-oo,-7] d [1,oo)

The function f: A->B defined by f(x)=-x^2+6x-8 is a bijection, if A=(-oo,\ 3] and B=(-oo,\ 1] (b) A=[-3,\ oo) and B=(-oo,\ 1] (c) A=(-oo,\ 3] and B=[1,\ oo) (d) A=[3,\ oo) and B=[1,\ oo)

If cos e c^(-1)(cos e cx) and cos e c(cos e c^(-1)x) are equal functions, then the maximum range of value of x is (a) [-pi/2,-1]uu[1,pi/2] (b) [-pi/2,0]uu[0,pi/2] (c) (-oo,-1)uu[1,oo] (d) [-1,0]uu[0,1]

VIKAS GUPTA (BLACK BOOK) ENGLISH-FUNCTION -SUBJECTIVE TYPE PROBLEMS
  1. If f:R->R where f(x) = ax + cosx is an invertible function, then (a)...

    Text Solution

    |

  2. Let f (x) be a polynomial of degree 6 with leading coefficient 2009, S...

    Text Solution

    |

  3. Let f(x)=x^(3)-3x+1. Then number of different real solutions of f(f(x)...

    Text Solution

    |

  4. If f(x+y+1)={sqrt(f(x))+sqrt(f(y))}^2 and f(0)=1AAx ,y in R ,d e t e ...

    Text Solution

    |

  5. If the domain of f(x) = sqrt (12-3^(x)-3^(3-x))+ sin ^(-1) ((2x)/(3 ...

    Text Solution

    |

  6. The number of elements in the range of the function : y =sin ^(-1) [...

    Text Solution

    |

  7. The number of integers in the range of function f(x)= [sinx] + [cosx] ...

    Text Solution

    |

  8. If P (x) is polynomial of degree 4 such than P (-1)=P (1) =5 and P (-2...

    Text Solution

    |

  9. The number of integral vlaue (s) of k for which the curve y = sqrt ( ...

    Text Solution

    |

  10. Let the solution set of the equation sqrt([x+[x/2]])+[sqrt({x})+[x/3]]...

    Text Solution

    |

  11. For the real number x, let f (x)=(1)/( ""^(2011sqrt(1-x^(2011)))). Fi...

    Text Solution

    |

  12. Find the number of elements contained in the range of the function f (...

    Text Solution

    |

  13. Let f (x,y)= x^(2) - y^(2) and g (x,y)=2xy. such that (f ( x,y))^(2) -...

    Text Solution

    |

  14. Let f (x) = (x+5)/(sqrt(x^(2) +1) ) , then the smallest integral va...

    Text Solution

    |

  15. The number of roots of equation (((x-1)(x-3))/((x-2)(x-4))-e^(x)) (((x...

    Text Solution

    |

  16. Let f (x) =x ^(2)-bx+c,b is an odd positive integer. Given that f (x)=...

    Text Solution

    |

  17. Let f(x) be a continuous function such that f(0) = 1 and f(x)=f(x/7)=x...

    Text Solution

    |

  18. If x=10 sum(r=3) ^(100) (1)/((r ^(2) -4)), then [x]= (where [.] deno...

    Text Solution

    |

  19. Let f(x)= cx+d/ax+b ​ . Then fof(x) = x provided that.

    Text Solution

    |

  20. Let A = {x|x ^(2) -4x+ 3 lt 0 , x in R} B={x|2^(1-x)+p le 0;x^2-2(p+7...

    Text Solution

    |

  21. Let the maximum value of expression y= (x ^(4)-x ^(2))/(x ^(6) + 2x ^(...

    Text Solution

    |