Home
Class 12
MATHS
Let f(x)={2/(1+x^2),xi sr a t ion a l b ...

Let `f(x)={2/(1+x^2),xi sr a t ion a l b ,xi sr a t ion a l` has exactly two points of continuity then the value of `b` are `(0,3]` b. `[0,1]` c. `(0,2]` d.`varphi`

A

(0,3]

B

[0,1]

C

(0,2]

D

`phi`

Text Solution

Verified by Experts

The correct Answer is:
C
`f(x)={{:((2)/(1+x^(2))",","x is irrational"),(b",","x is rational"):}` has exactly two points of continuity then equation `(2)/(1+x^(2))=b` must have two distinct roots.
Now `(2)/(1+x^(2)) in(0,2]`
`rArr" "b in {0,2]`
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    CENGAGE|Exercise Multiple Correct Answer Type|9 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    CENGAGE|Exercise Comprehension Type|2 Videos

  • CONIC SECTIONS

    CENGAGE|Exercise Solved Examples And Exercises|91 Videos

  • COORDINATE SYSTEM

    CENGAGE|Exercise Multiple Correct Answers Type|2 Videos

Similar Questions

Explore conceptually related problems

Discuss the continuity of f(x)={x^2,xi sr a t ion a l-x^2,xi si r r a t ion a ldot

Find the value of x where f(x)={x ,ifxi sr a t ion a l1-x ,ifxi si r r a t ion a li scon t inuou sdot

Let f(x)={(1)/(x^(2))int_(0)^(x)sin(t^(2))dt for x!=0(a in R) and a,for x=0 If f(x) is continuous at x=0, then the value of a is

Let f(x)=x+2|x+1|+2|x-1|* If f(x)=k has exactly one real solution,then the value of k is (a) 3 (b) 0(c)1(d)2

For f(x)={[x^(3),,x =1] , LMVT holds on [0,2] . The value of b and the value of c in (0,2) is

Let f(x)=[((x^2+3x-1)t a n x)/(x^2+2x)\ if\ x!=0,kif\ x=0 f(x) is continuous , then find the value of kdot

Let f(x)=(1+b^(2))x^(2)+2bx+1 and let m(b) the minimum value of f(x) as b varies, the range of m(b) is (A) [0,1](B)(0,(1)/(2)] (C) [(1)/(2),1](D)(0,1]

If f(x)=(1-cos2x)/(x^(2)) , x!=0 and f(x) is continuous at x=0 ,then f(0)= (a) 1 (b) 2 (c) 3 (d) None of these

CENGAGE-CONTINUITY AND DIFFERENTIABILITY-Question Bank
  1. Let f(x)={2/(1+x^2),xi sr a t ion a l b ,xi sr a t ion a l has exactly...

    Text Solution

    |

  2. Let f(x) = {(x^(2)-a, if x lt 3),(bsqrt(x-2)+a, if 3 le x lt 6),(2x+b,...

    Text Solution

    |

  3. Given f(x) = {(x^(2)-5x+alpha, -ooltxle 0),(|7-3x|+sin [x], o lt x lt ...

    Text Solution

    |

  4. Let f(x) = {(sqrt(x^(2)-1), x le sqrt10),((sqrt(10x)-7), sqrt10lt xlt...

    Text Solution

    |

  5. Let f(x) = sqrt(x^(2)+px+1)/(x^(2)-p). If f(x) is discontinuous at exa...

    Text Solution

    |

  6. Number of points of non-derivability of the function f(x) = root (3)((...

    Text Solution

    |

  7. If f(x) = {(lim(x rarr oo)(6^(t)+10^(t))^(1/t), x = 0),(x^(2)+4x+C, x ...

    Text Solution

    |

  8. Number of point(s) in [1,2] where f(x) = (-2)^([x^(3)]) is non-differe...

    Text Solution

    |

  9. Consider the function f(x) = {(a^(2)+e^(x), -oo lt x lt 0),(x+2, 0le x...

    Text Solution

    |

  10. Let f(x) = [(sqrt(1+sin^(2)(x^(2))-cos^(3)(x^(2)))/(x^(3)tanx), if x n...

    Text Solution

    |

  11. Let f(x) = {(cos(x^(3)), -ooltxlt0),(sin(x^(3))-|x^(3)-1|, 0lexltoo):}...

    Text Solution

    |

  12. The sum of all values of x for which the function f(x) = sqrt(|x^(2)-5...

    Text Solution

    |

  13. Let f(x) = [(-1, -3 le x lt 0),(x-1, 0le xle 3):} and g(x) = f(|x|)+|f...

    Text Solution

    |

  14. Let f(x) be a differentiable function satisfying f((x+2y)/3)= (f(x)+2f...

    Text Solution

    |

  15. Let f(x) = {((sin alphax^(2))/x^(2), x ne 0),(3/4+1/(4alpha), x = 0):}...

    Text Solution

    |

  16. Let f(x) = {(a tan^(-1)(1/(x-4)), 0 lexlt4),(pi/2, x= 4),(btan^(-1)(2/...

    Text Solution

    |

  17. Let f(x) = {((1+ax)^(1/x), x lt 0),((root(3)(x+c)-1)/(sqrt(x+1)-1), x ...

    Text Solution

    |

  18. The number of points in (-5,5) where f(x)=[x](x^(3)-x)^(2)) is non-dif...

    Text Solution

    |

  19. If f(x) = cos (x (cos)1/x) and g(x) = (In(sec^(2)x))/(x sin x) are bot...

    Text Solution

    |

  20. Consider , f(x) = {(|(x-x^(3) 1 2),(0 2 3x^(4)),(x^(2) 4x x^(3)-3x^(5)...

    Text Solution

    |

  21. Number of points where f(x)= max {2-|x|, min {x^(2)-1}} is not differe...

    Text Solution

    |