Home
Class 12
MATHS
Find the range of f(x)=cos^(-1)((sqrt(1+...

Find the range of `f(x)=cos^(-1)((sqrt(1+2x^2))/1)`

Text Solution

Verified by Experts

`f(x)="cos"^(-1)((sqrt(1+2x^(2)))/(1+x^(2)))`
`="sin"^(-1)(sqrt(1-(1+2x^(2))/((1+x^(2))^(2))))( :' cos^(-1)x=sin^(-1)sqrt(1-x^(2)))`
`="sin"^(-1)(sqrt((x^(4))/((1+x^(2))^(2))))`
`="sin"^(-1)((x^(2))/(1+x^(2)))`
`="sin"^(-1)(1-(1)/(1+x^(2)))`
Now, `(1-(1)/(1+x^(2))) in [0,1)`
` :. f(x) in [0,(pi)/(2))`
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise 1.1|15 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise 1.2|5 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise JEE Previous Year|12 Videos

  • Quadratic Equations, Inequalities, Modulus and Logarithms

    CENGAGE|Exercise Question Bank|28 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

Find the range of f(x)=1/(2cosx-1)

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

Find the range of f(x)=tan^(-1)sqrt((x^2-2x+2))

Find the range of f(x) = sqrt(x-1)+sqrt(5-x)

Find the range of f(x)=sqrt(4-sqrt(1+tan^2x)) .

Find the range of f(x)=1/(1-3sqrt(1-sin^2x))

Find the range of f(x)=sqrt(1-sqrt(x^2-6x+9))

Find the range of f(x)=1/(2abscosx-3)

Find the range of f(x)=cos^2x+sec^2x .

Find the range of f(x)=sin^2x-sinx+1.

CENGAGE-RELATIONS AND FUNCTIONS-Examples
  1. Find the range of tan^(-1)((2x)/(1+x^2))

    Text Solution

    |

  2. Find the range of f(x)=cot^(-1)(2x-x^2)dot

    Text Solution

    |

  3. Find the range of f(x)=cos^(-1)((sqrt(1+2x^2))/1)

    Text Solution

    |

  4. Find the domain of f(x)=sqrt(((1-5^x)/(7^(-1)-7)))

    Text Solution

    |

  5. Find the domain of f(x)=sqrt((0. 625)^(4-3x)-(1. 6)^(x(x+8)))

    Text Solution

    |

  6. Is the pair of the functions e^(sqrt(log(e)x)) and sqrt(x) identical ?

    Text Solution

    |

  7. Find the domain and range of following functions (i) f(x)=log(e)(sin...

    Text Solution

    |

  8. Range of the function : f(x)=log2((pi+2sin^(- 1)((3-x)/7))/pi)

    Text Solution

    |

  9. Find the domain of f(x)=(log)(10)(log)2(log)(2/pi)(t a n^(-1)x)^(-1)

    Text Solution

    |

  10. Find the domain and range of f(x)=sqrt((log)3{"cos"(sinx)})

    Text Solution

    |

  11. Find the domain of f(x)=sin^(-1){(log)9((x^2)/4)}

    Text Solution

    |

  12. Find the domain of function f(x)=(log)4[(log)5{(log)3(18 x-x^2-77}]

    Text Solution

    |

  13. Let x= in (0,pi/2)dot Then find the domain of the function f(x)=1/(-(l...

    Text Solution

    |

  14. Find the domain of f(x)=sqrt((log)(0. 4)((x-1)/(x+5)))

    Text Solution

    |

  15. Find the range of f(x)=(log)e x-((log)e x)hat2)/(|(log)e x)

    Text Solution

    |

  16. If f(x)=sin(log)e{(sqrt(4-x^2))/(1-x)} , then the domain of f(x) is a...

    Text Solution

    |

  17. Find the domain of the function f(x)=(1)/([x]^(2)-7[x]-8), where [.] r...

    Text Solution

    |

  18. Find the domain of f(x)=sqrt(([x]-1))+sqrt((4-[x])) (where [ ] repres...

    Text Solution

    |

  19. Find the domain and range of f(x)=sin^(-1)[x]w h e r[] represents the ...

    Text Solution

    |

  20. If [cot^(-1)x]+[cos^(-1)x]=0 , where [] denotes the greatest integer f...

    Text Solution

    |