Home
Class 12
MATHS
The range of f(x)=cos^(-1)((1+x^3)/(x2))...

The range of `f(x)=cos^(-1)((1+x^3)/(x2))+sqrt(2-x^2)` is `{0,1+pi/2}` (b) `{0,1+pi)` `{1,1+pi/2}` (d) `{1,1+pi}`

A

`{0,1+(pi)/(2)}`

B

`{0,1+pi}`

C

`{1,1+(pi)/(2)}`

D

`{1,1+pi}`

Text Solution

Verified by Experts

The correct Answer is:
D
`cos^(-1)((1+x^(2))/(2x)) " is defined if " |(1+x^(2))/(2x)| le 1 " and " x ne 0`
or ` 1+x^(2) -2|x| le 0`
or ` (|x|-1)^(2) le 0`
or `x=1, -1`
Thus, the domain of `f(x)` is `{1,-1}`. Hence, the range is `{1,1+pi}.`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|3 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE PUBLICATION|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

The range of f(x)=cos^(-1)((1+x^2)/(2x))+sqrt(2-x^2) is {0,1+pi/2} (b) {0,1+pi) {1,1+pi/2} (d) {1,1+pi}

The range of f(x)=sin^(-1)((x^2+1)/(x^2+2)) is (a) [0,pi/2] (b) (0,pi/6) (c) [pi/6,pi/2] (d) none of these

The range of f(x)=sin^(-1)(sqrt(x^2+x+1)) i s (a) (0,pi/2) (b) (0,pi/3) (c) [pi/3,pi/2] (d) [pi/6,pi/3]

Find the range of f(x) = (sin^(-1) x)^(2) + 2pi cos^(-1) x + pi^(2)

Prove that : cos^(-1) x + cos^(-1) ((x)/(2) + (sqrt( 3-3x^2) )/( 2) ) = (pi)/ (3)

If x<0, then prove that cos^(-1)x=pi-sin^(-1)sqrt(1-x^2)

Range of tan^(-1)((2x)/(1+x^2)) is (a) [-pi/4,pi/4] (b) (-pi/2,pi/2) (c) (-pi/2,pi/4) (d) [pi/4,pi/2]

The value of cos^(-1)sqrt(2/3)-cos^(-1)((sqrt(6)+1)/(2sqrt(3))) is equal to (A) pi/3 (B) pi/4 (C) pi/2 (D) pi/6

The number of solutions of the equation cos^(-1)((1+x^2)/(2x))-cos^(-1)x=pi/2+sin^(-1)x is 0 (b) 1 (c) 2 (d) 3

The range of the function tan^(-1)((x^2+1)/(x^2+sqrt(3))),x in R is a. [pi/6,pi/2) b. [pi/6,pi/3) c. [pi/6,pi/4] d. none of these

CENGAGE PUBLICATION-RELATIONS AND FUNCTIONS-All Questions
  1. Range of function f(x) = cos (k sin x) is [-1, 1], then the least posi...

    Text Solution

    |

  2. Let f(x)=sqrt(|x|-|x+)(w h e r e{dot} denotes the fractional part of (...

    Text Solution

    |

  3. The range of f(x)=cos^(-1)((1+x^3)/(x2))+sqrt(2-x^2) is {0,1+pi/2} (b...

    Text Solution

    |

  4. The range of the following function is f(x)=sqrt((1-cosx)sqrt((1-cosx)...

    Text Solution

    |

  5. The range of f(x)=(x+1)(x+2)(x+3)(x+4)+5 for x in [-6,6] is [4, 5045] ...

    Text Solution

    |

  6. The range of f(x)=sec^(-1)((log)3tanx+(log)(tanx)3) is (a) [pi/3,pi/2...

    Text Solution

    |

  7. The domain of definition of the function f(x)={x}^({x})+[x]^([x]) is w...

    Text Solution

    |

  8. 49. If [x^2-2x + a] = 0 has no solution then

    Text Solution

    |

  9. The value of sum(r=1)^(2000) {{x+r}}/2000 is

    Text Solution

    |

  10. If f(x)=(sin([x]pi))/(x^2+x+1) , where [dot] denotes the greatest inte...

    Text Solution

    |

  11. Let f(x)=([a]^2-5[a]+4)x^3-(6{a}^2-5{a}+1)x-(tanx)xsgnx be an even fun...

    Text Solution

    |

  12. The solution set for [x]{x}=1 (where {x} and [x] are respectively, fra...

    Text Solution

    |

  13. Let [x] represent the greatest integer less than or equal to x If [sqr...

    Text Solution

    |

  14. The number of roots of x^2-2=[sinx],w h e r e[dot] stands for the grea...

    Text Solution

    |

  15. The domain of f(x)=sin^(-1)[2x^2-3],w h e r e[dot] denotes the greates...

    Text Solution

    |

  16. The domain of f(x)=sqrt(2{x}^2-3{x}+1), where {.} denotes the fraction...

    Text Solution

    |

  17. Find the range of the following function f(x)=sin^(-1)[x^2+1/2]+cos^(...

    Text Solution

    |

  18. Let f(x)=e^({e^(|x|sgnx)})a n dg(x)=e^([e^(|x|sgnx)]),x in R , where ...

    Text Solution

    |

  19. Number of solutions of the equation, [y+[y]]=2cosx is: (where y=(1//3)...

    Text Solution

    |

  20. The function f(x)=sin(log(x+sqrt(1+x^2))) is (a) even function (b) odd...

    Text Solution

    |