Home
Class 12
MATHS
If the function f(x)={(Ax-B ,, x le 1),...

If the function `f(x)={(Ax-B ,, x le 1),(3x ,,1 lt x lt 2),(Bx^2-A ,, x ge 2):}`
is continuous at `x=1` and discontinuous at `x=2`,
find the values of `A and B`.

Promotional Banner

Topper's Solved these Questions

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|102 Videos

  • COORDINATE SYSTEM

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|2 Videos

Similar Questions

Explore conceptually related problems

Examine the function, f(x)={(x-1, x lt 0),(1//4, x=0), (x^2-1, xgt 0):} Discuss the continuity, and if discontinuous remove the discontinuity.

Let f(x) = {(ax+1, x lt 1), (3, x=1), (bx^2+1, x gt 1):} . For what values of a and b is f(x) continuous at x = 1 ?

If the relation f(x)={(2x-3",",x le 2),(x^(3)-a",",x ge2):} is a function, then find the value of a.

If the function f(x)={{:(3ax+b,"for "xgt1),(" " 11,"when " x=1),(5ax-2b,"for " xlt1):} is continuous at x = 1 , find the values of a and b .

A function f (x) is defined as follows : f(x)={{:(3x+1,"for "xle1 ),(3-ax^(2),"for " xgt1):} If f (x) is continuous at x = 1 , find the value of a.

If f(x)={(5+x^2, x lt 1), (x-4, x ge 1):} is jump discontinuous, then the number of jumps must be

Find the range of the function f(x) = abs(x - 1) + abs(x - 2) , -1 le x le 3

Let f(x)={(1+x, 0 le x le 2), (3-x, 2 lt x lt 3):} Discuss the continuity of f, f' on [0, 2].

Let f(x) = {((x^2-4)/(x+2), x lt -3), (Ina, x=-3), (a+bx, x gt -3):} . For what value of a and b is f(x) continuous on the real line?

If f (x) ={{:(x",", "when " 0 lt x lt 1),(2-x",", "when" 1 lt x le 2):} then f'(1) is equal to-

CENGAGE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. What value must be assigned to k so that the function f(x)={(x^4-25...

    Text Solution

    |

  2. Let f(x) be a function defined as f(x)={(x^2-1)/(x^2-2|x-1|-1),x!=1 ...

    Text Solution

    |

  3. If the function f(x)={(Ax-B ,, x le 1),(3x ,,1 lt x lt 2),(Bx^2-A ,, ...

    Text Solution

    |

  4. Let : f(x)={((a+3cosx)/(x^2) ,, x<0),(btan(pi/([x+3])) ,, xgeq0):} If...

    Text Solution

    |

  5. Let : f(x)={(sina x^2)/(x^2),x!=0 3/4+1/(4a),x=0 for what values of...

    Text Solution

    |

  6. f(x)={|x+1|;xlt=0x ;x >0 and g(x)={|x|+1;xlt=1-|x-2|;x >1 Draw its g...

    Text Solution

    |

  7. f(x)={cos^(-1){cotx), x<pi/2 pi[x]-1, x >pi/2 where [dot] represe...

    Text Solution

    |

  8. Discuss the differentiability of f(x)=|(log)ex| ,x>0

    Text Solution

    |

  9. Discuss the differentiability of f(x)="max"{sec^(-1)x , cosec^(-1)x}

    Text Solution

    |

  10. A function f(x) is such that f(x+pi/2)=pi/2-|x|AAx. Find f(pi/2), if i...

    Text Solution

    |

  11. Discuss the differentiability of f(x)=|x-1|+|x+1|

    Text Solution

    |

  12. Which of the function is non-differential at x=0? f(x)=|"x"^3|

    Text Solution

    |

  13. Discuss the differentiability of f(x)=|x^3| at x=0

    Text Solution

    |

  14. Discuss the differentiability of f(x)=|x|sinx+|x-2|sgn(x-2)+|x-3|dot

    Text Solution

    |

  15. Discuss the differentiability of f(x)="sin"|x|

    Text Solution

    |

  16. Discuss the differentiability of f(x)=[x]+|1-x|, x in (-1,3),w h e r e...

    Text Solution

    |

  17. Discuss the differentiability of f(x)=(x^2-1)|x^2-x-2|+sin(|x|)dot

    Text Solution

    |

  18. Let f be a function satisfying f(x+y)+sqrt(6-f(y))=f(x)f(y)a n df(h)->...

    Text Solution

    |

  19. Let f(x+y)=f(x)+f(y) for all xa n dydot If the function f(x) is contin...

    Text Solution

    |

  20. A function f(x) satisfies the following property: f(x+y)=f(x)f(y)dot S...

    Text Solution

    |