Home
Class 12
MATHS
If the function f(x) ={(ax-b, x le1),(3x...

If the function `f(x) ={(ax-b, x le1),(3x, 1lt x lt 2),(bx^(2)-a, x ge 2):}` is continuous at x =1 and discontinuous at x =2, then

A

a = 3+b, b =3

B

a = 3+b

C

`a = 3+b, b ne 3`

D

`a ne 3+b, b =3`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|219 Videos

  • LINEAR INEQUALITIES

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|54 Videos

Similar Questions

Explore conceptually related problems

If f(x) = {(x-5,x le1),(4x^(2)-9, 1ltxlt2),(3x+4, x ge2):} then f^(')(2^(+)) =

Find the values of a and b such that the function defined by f(x) = {(5,if, x le2),(ax + b,if, 2 lt x lt 10),(21,if,xge10):} is continuous function.

If f(x) ={((sqrt(1+kx)- sqrt(1-kx))/x, -1 le x le0),(2x^(2)+3x-2, 0 lex le1):} is continuous at x = 0, thenk =

The value of b for which the function : f(x) = {{:(5x-4,"if",0lt x le 1),(4x^(2)+3bx,"if",1 lt x lt 2):} is continuous at every point of its domain is :

Is the function defined by f(x)={{:(x+5," if "x le1),(x-5," if "x gt 1):} a continuous function?

If the function . f(x) = 4 xx 5^(x) for x lt 0 = 8a + x for x ge 0 , is continuous , then the value of a is

Is the function f defined by f(x) = {{:(x," if "x le 1),(3," if "x gt 1):} continuous at x= 0 ? At x=1? At x=2? .

If F(x)= {(Kx^(2) if x le 2),(3 if x gt 2):} is continuous at x = 2, then the value of K is

If f(x)={{:(Kx^(2),"if x" le 2),(3,"if x" gt 2):}} is continuous at x = 2, then the value of K is

HIMALAYA PUBLICATION-LIMITS, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. Let f(x) = (1 - cos px)/(x sin x), where x ne 0 and f(0) = (1)/(2). If...

    Text Solution

    |

  2. Let f(x) = [(x^(2),x le 0),(ax + b, x gt 0)]lim The values of a and b ...

    Text Solution

    |

  3. If the function f(x) ={(ax-b, x le1),(3x, 1lt x lt 2),(bx^(2)-a, x ge ...

    Text Solution

    |

  4. y = tan^(-1)((3x-x^3)/(1-3x^2)), 1/(sqrt3) , x , 1/(sqrt3).

    Text Solution

    |

  5. f(x) = {((sin 2x)^(tan^(2)2x), x ne pi/4),(k, x = pi/4):}. If f(x) is ...

    Text Solution

    |

  6. If f(x) = {((x^(5)-32)/(x-2), x ne 2),(k, x =2):} is continuous at x =...

    Text Solution

    |

  7. If the function f(x) = [((cos x)^(1//x),x ne 0),(k,x = 0):} is continu...

    Text Solution

    |

  8. If f(x) ={(3x-4, 0lexle2),(2x+lambda, 2ltxle3):} is continuous at x = ...

    Text Solution

    |

  9. If f(x) = (2x^(3)-ax+3)/(x-3) is continuous at x = 3, then

    Text Solution

    |

  10. If [x]^(2)-5[x]+6=0, where [.] denotes the greatest integer function, ...

    Text Solution

    |

  11. lim(x rarr oo) (log x)/([x]), where [.] denotes the greatest integer f...

    Text Solution

    |

  12. If f(x) is an odd function and lim(x rarr 0) f(x) exists, then lim(x r...

    Text Solution

    |

  13. lim(x rarr 0) (sin x)/(x (1 + cos x)) is equal to :

    Text Solution

    |

  14. lim(x rarr (pi)/(2)) (1-sin x)/(cos x) is equal to :

    Text Solution

    |

  15. lim(x rarr 0) (|x|)/(x) is equal to :

    Text Solution

    |

  16. lim(x rarr 1) [x-1], where [*] is the greatest integer function is equ...

    Text Solution

    |

  17. lim(x rarr 0)"x sin" (1)/(x) is equal to :

    Text Solution

    |

  18. lim(n rarr oo) (1+2+3+…...+n)/(n^(2)), n in N is equal to :

    Text Solution

    |

  19. lim(x rarr pi) (sin x)/(x - pi) is

    Text Solution

    |

  20. lim(x rarr 0) (x^(2) cos x)/(1- cos x) is

    Text Solution

    |