Home
Class 12
MATHS
Find the range of tan^(-1)((2x)/(1+x^2))...

Find the range of `tan^(-1)((2x)/(1+x^2))`

Text Solution

Verified by Experts

First, we must get the range of
`(2x)/(1+x^(2))=y`
We have `yx^(2)-2x+y=0`
Since x is real, `D ge 0, " i.e., "4-4y^(2) ge 0 " or " -1 le y le 1.` So,
` "tan"^(-1)(y) in [-(pi)/(4),(pi)/(4)]` (As `tan x` is an increasing function)
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 cot^(-1)(2x-x^2)

Find the derivative of tan^(-1)(2x)/(1-x^2)wdotrdottsin^(-1)(2x)/(1+x^2)

Find the range of f(X) = tan^(-1)x-(1)/(2)log_(e)x in (1)/(sqrt(3)),(sqrt(3))

Find the derivative of sin^(-1)((2x)/(1+x^(2))) with respect to tan^(-1)x .

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

If x in (0, 1) , then find the value of tan^(-1) ((1 -x^(2))/(2x)) + cos^(-1) ((1 -x^(2))/(1 + x^(2)))

Find the derivative of sin^(-1) ((2x)/(1+x^2)) with respect to tan^(-1) x .

Find the derivative of tan^(-1) ( 1 + x^2) with respect to x^2 + x + 1 .

Find the range of f(x)=(x^2+1)/(x^2+2)

CENGAGE-RELATIONS AND FUNCTIONS-Examples
  1. Find the range of f(x)=sin^(-1)x+tan^(-1)x+cos^(-1)xdot

    Text Solution

    |

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

    Text Solution

    |

  3. Find the range of tan^(-1)((2x)/(1+x^2))

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |