Home
Class 12
MATHS
The function f(x)={{:((pi)/(4)+tan^(-1)x...

The function `f(x)={{:((pi)/(4)+tan^(-1)x",",|x|le1),((1)/(2)(|x|-1)",",|x|gt1):}` is :

A

continuous on `R-{-1}` and differentiable on `R-{-1, 1}`.

B

both continuous and differentiable on `R-{-1}`

C

continuous on `R-{1}` and differentiable on `R-{-1, 1}`.

D

both continuous and differentiable on `R-{1}.`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • JEE MAINS

    JEE MAINS PREVIOUS YEAR|Exercise Physics|30 Videos

  • JEE MAINS 2021

    JEE MAINS PREVIOUS YEAR|Exercise Mathematics (Section A )|20 Videos

Similar Questions

Explore conceptually related problems

The domain of the derivative of the function: f(x)={{:(,tan^(-1)x,|x| le1),(,(1)/(2)(|x|-1),|x|gt1):}

The domain of the derivation of the functions f(x) = {{:(tan^(_1) x", if " |x|le1),(" is"),(1/2(|x|-1)", if "|x| gt 1):}

Discuss the continuity of the function f(x) ={:{((1+cos x)/(tan^2 x) ", "x ne pi),((1)/(2) ", " x=pi):}, at =pi .

Let f(x)=f_(1)(x)-2f_(2)(x), where f_(1)(x)={{:(min{x^(2),|x|}",",|x|le1),(max{x^(2),|x|}",",|x|gt1):} "and "f_(2)(x)={{:(min {x^(2),|x|}",",|x|gt1),(max{x^(2),|x|}",",|x|le1):} "and let "g(x)={{:(min{f(t),-3letlex,-3lexlt0}),(max{f(t),0letltx,0lexle3}):} For x in(-1,00),f(x)+g(x) is

Let f(x)=f_(1)(x)-2f_(2)(x), where f_(1)(x)={{:(min{x^(2),|x|}",",|x|le1),(max{x^(2),|x|}",",|x|gt1):} "and "f_(2)(x)={{:(min {x^(2),|x|}",",|x|gt1),(max{x^(2),|x|}",",|x|le1):} "and let "g(x)={{:(min{f(t),-3letlex,-3lexlt0}),(max{f(t),0letltx,0lexle3}):} The graph of y=g(x) in its domain is broken at

Let f(x) be a continuous function fiven by f(x)={(2x",", |x|le1),(x^(2)+ax+b",",|x|gt1):},"then " If f(x) is continuous for all real x then the value of a^(2)+b^(2) is

JEE MAINS PREVIOUS YEAR-JEE MAINS 2020-MATHEMATICS
  1. If a and b are real numbers such that (2+alpha)^(4)=a+balpha, where al...

    Text Solution

    |

  2. The solution of the differential equation (dy)/(dx)-(y+3x)/(log(e)(y+3...

    Text Solution

    |

  3. The function f(x)={{:((pi)/(4)+tan^(-1)x",",|x|le1),((1)/(2)(|x|-1)","...

    Text Solution

    |

  4. Center of a circle S passing through the intersection points of circle...

    Text Solution

    |

  5. Let x=4 be a directrix to an ellipse whose centre is at the origin and...

    Text Solution

    |

  6. The distance of the point (1,-2,3) from the plane x-y+z=5 measured par...

    Text Solution

    |

  7. The minimum value of 2^(sinx)+2^(cosx) is -

    Text Solution

    |

  8. Find the equation of the perpendicular bisector of the line segment ...

    Text Solution

    |

  9. The sum of the series (2.^1P0-3.^2P1+4^3P2-5.^4P3+.....51 terms) +(1!-...

    Text Solution

    |

  10. Let P be a point on the parabola, y^(2)=12x and N be the foot of the p...

    Text Solution

    |

  11. Matrix was given as det [[x-2,2x-3,3x-4],[2x-3,3x-4,4x-5],[3x-5,5x-8,1...

    Text Solution

    |

  12. The foot of the perpendicular drawn form the point (4,2,3) to the line...

    Text Solution

    |

  13. If y^(2)+log(e)(cos^(2)x)=yx in (-(pi)/(2),(pi)/(2)), then

    Text Solution

    |

  14. Solve : 2pi-(sin^(-1)(4/5)+sin^(-1)(5/13)+sin^(-1)(16/65))=

    Text Solution

    |

  15. The length of transverse axis of a hyperbola is sqrt(2). The foci of h...

    Text Solution

    |

  16. For the frequency distribution: {:("Variate (x): " x(1)" "x(2)"...

    Text Solution

    |

  17. A die is thrown two times and the sum of the scores appearing on the d...

    Text Solution

    |

  18. The number of integral terms in the expansion of (sqrt(3)+root(5) (8))...

    Text Solution

    |

  19. int(-pi)^(pi)|pi-|x||dx

    Text Solution

    |

  20. If A={m: both roots of x^2-(m+1)x+m+4=0 is real} and B=[-3,5) which of...

    Text Solution

    |