Home
Class 11
MATHS
Let f(x) = {((x^2-4)/(x+2), x lt -3), (I...

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?

Text Solution

Verified by Experts

`a=e^(-5), b=1/3(5+e^(-5))`
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

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 f(x)={(x^3, x gt 0),(0, x=0),(-x^3, x lt0):}

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

If f(x)= {((tan 3x)/(4x),xne0 ),(k, x=0):} , then for what value of K, f(x) is continuous.

Let f(x)={((x-4)/(|x-4|)+a, xlt4),(a+b, x=4),((x-4)/(|x-4|)+b,x gt 4):} Then , f (x) is continuous at x = 4, when

Let f(x)= {(a|x^2-x-2| /(2+x-x^2) , xlt2),(b, x = 2), ((x-[x])/(x-2), x gt 2):} If f(x) is continuous at x = 2 , (where [.] denotes greatest integer function) : then (a , b ) is ,

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 .

For what value of f (4) the function f(x)=(x^(2)-16)/(x-4) is continuous at x = 4 ?

The function f(x)=(x^(2)-4)/(x^(3)-8) is undefined at x =1 , what should be the value of f (1) such that f (x) may be continuous at x =1 ?

f(x)=(x^2-1)/(x^3-1) is undefined at x=1. What should be the value of f(x) at x=1 such that f(x) may be continuous at x=1?

PATHFINDER-LIMIT, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. Find the set of points where the following functions are discontinuous...

    Text Solution

    |

  2. Find the set of points where the following functions are discontinuous...

    Text Solution

    |

  3. Let f(x) = {((x^2-4)/(x+2), x lt -3), (Ina, x=-3), (a+bx, x gt -3):}. ...

    Text Solution

    |

  4. Let f(x) = {(ax+1, x lt 1), (3, x=1), (bx^2+1, x gt 1):}. For what val...

    Text Solution

    |

  5. Let f be a twice differentiable function such that f"(x) = -f(x) , and...

    Text Solution

    |

  6. If |c|le1/2 and f(x) is a differentiable function at x = 0 given by ...

    Text Solution

    |

  7. Let f(x)={(x+a if x lt 0), (|x-1| if x ge 0):} and g(x)={(x+1 if x lt ...

    Text Solution

    |

  8. f is a function such that f(x + y) = f(x) .f(y),forall x, y in R , if ...

    Text Solution

    |

  9. A real valued function satisfies the relation f(x+y)=f(x)+f(y)+(e^x-1)...

    Text Solution

    |

  10. If f(x)f(y) + 2 = f(x) + f(y) + f(xy) and f(1) = 2, f'(1) = 2, then fi...

    Text Solution

    |

  11. Let f(x)={(1+x, 0 le x le 2), (3-x, 2 lt x lt 3):} Determine the for...

    Text Solution

    |

  12. Let f(x)={(1+x, 0 le x le 2), (3-x, 2 lt x lt 3):} Discuss the conti...

    Text Solution

    |

  13. Let f(x)={(x exp[-(1/|x|+1/x)], x ne 0),(0, x=0):} Test whether f(x)...

    Text Solution

    |

  14. Let a and b be real numbers such the the function f(x)={(-3ax^2-2,x<1...

    Text Solution

    |

  15. Let m and n be two positive integers greater than 1. if lim(alphararr0...

    Text Solution

    |

  16. The correct statement(s) is (are)

    Text Solution

    |

  17. Let f(x) be a polynomial of degree four having extreme values at x=1 a...

    Text Solution

    |

  18. lim(xrarr0)((1-cos2x)(3+cosx))/(xtan4x) is equal to:

    Text Solution

    |

  19. If the function . g(x)={(ksqrt(x+1),0lexle3),(mx+2,3ltxle5):}is differ...

    Text Solution

    |

  20. Let f:RrarrR be defined as . f(x)={(0, "x is irrational"),(sin|x|,"x i...

    Text Solution

    |