Home
Class 12
MATHS
Indicate all correct alternatives if, f(...

Indicate all correct alternatives if, `f(x) = x/2-1`, then on the interval `[0, pi]`

A

`tan (f(x)) and (1)/(f(x))` are both continuous

B

`tan (f(x)) and (1)/(f(x))` are both discontinuous

C

`tan (f(x)) and f^(-1)(x)` are both continuous

D

`tan(f(x))` is continuous but `(1)/(f(x))` is not continuous

Text Solution

Verified by Experts

The correct Answer is:
C, D
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|11 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|16 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (Single Option Correct Type Questions)|50 Videos
  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|43 Videos
  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

Similar Questions

Explore conceptually related problems

If f (x) = 1/2 x - 1 , then on the interval [0, pi]

The maximum value of f(x) =2 sin x + sin 2x , in the interval [0, (3)/(2)pi] is

Find the maximum and minimum values of f(x)=x+sin2x in the interval [0,2 pi]

Verify Rolle's Theorem for the function : f(x) = sin x + cos x in the interval [0,2pi]

Verify Rolle's theorem for the following functions in the given intervals. f(x) sin x in the interval [ 0, pi] .

Verify Rolle's theorem for the following functions in the given intervals. f(x) = sinx + cos x in the interval [0 , pi//2] .

ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (More Than One Correct Option Type Questions)
  1. Function whose jump (non-negative difference of LHL and RHL) of discon...

    Text Solution

    |

  2. Indicate all correct alternatives if, f(x) = x/2-1, then on the interv...

    Text Solution

    |

  3. On the interval I=[-2,2], the function f(x)={{:(,(x+1)e^(-((1)/(|x|)+(...

    Text Solution

    |

  4. Given f(x)={3-[cot^(-1)((2x^3-3)/(x^2))]forx >0{x^2}cos(e^(1/x))forx<0...

    Text Solution

    |

  5. If f(x) = {{:(b([x]^(2)+[x])+1",","for",x gt -1),(sin(pi(x + a))",","f...

    Text Solution

    |

  6. Q. For every integer n, let an and bn be real numbers. Let function f:...

    Text Solution

    |

  7. If f(x) = |x+1|(|x|+|x-1|), then at what points the function is/are no...

    Text Solution

    |

  8. Let [x] be the greatest integer function f(x)=(sin(1/4(pi[x]))/([x])) ...

    Text Solution

    |

  9. If f(x) = {{:((sin^(-1)x)^(2)cos((1)/(x))",",x ne 0),(0",",x = 0):} th...

    Text Solution

    |

  10. Q. Let f(x)=cos x $ H(x)=[min [f(t) 0&lt;=t&lt;=x for 0&lt;=x&lt;=p...

    Text Solution

    |

  11. If f(x) = 3(2x + 3)^(2//3) + 2x + 3, then

    Text Solution

    |

  12. "If "f(x)={{:(,-x-(pi)/(2),x le -(pi)/(2)),(,-cos x,-(pi)/(2) lt x le ...

    Text Solution

    |

  13. If f(x)={{:(,(x log cos x)/(log(1+x^(2))),x ne 0),(,0,x=0):} then

    Text Solution

    |

  14. Let [x] denotes the greatest integer less than or equal to x. If f(x) ...

    Text Solution

    |

  15. The function, f(x)=[|x|]-|[x]| where [] denotes greatest integer funct...

    Text Solution

    |

  16. The function f(x)=sqrt(1-sqrt(1-x^2))

    Text Solution

    |

  17. Consider the function f(x) = |x^(3) + 1|. Then,

    Text Solution

    |

  18. f is a continous function in [a, b]; g is a continuous function in [b,...

    Text Solution

    |

  19. Which of the following function(s) has/have the same range ?

    Text Solution

    |

  20. If f(x) = sec 2x + cosec 2x, then f(x) is discontinuous at all points ...

    Text Solution

    |