Home
Class 11
MATHS
Let f(x) = {(ax+1, x lt 1), (3, x=1), (b...

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 ?

Text Solution

Verified by Experts

a = 2, b = 2
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

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 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 .

Let f(x) = x(1/(x - 1) + 1/x + 1/(x + 1)), x gt 1 , Then

If f(x)=ax^(2)+bx+c and f(x - 1) = f(x) + 2x + 1. then find the values of a and b.

If f(x)=ax^(2)+bx+c and f(x + 1) = f(x) + x + 1, then determine the values of a and b.

Let g(x)=1+x-[x] and f(x)=={(-1, x lt0),(0, x=0),(1, x gt 0):} Then for all x find f(g(x))

If f(x)={(-1, xlt0 ),(0, x =0),(1, x gt 0):} and g(x)=x(1-x^2), then , f(g(x)) is continuous for,

Let f(x)=x((1)/(x-1)+(1)/(x)+(1)/(x+1)), x gt 1 . Then

Draw the graph of the function : f(x)=1+2x," when "xle1 =3-x," when "x gt1 From the graph examine whether f(x) is continuous at x = 1 or not.

Let f(x)={(log(1+x)^(1+x)-x)/(x^2)}dot Then find the value of f(0) so that the function f is continuous at x=0.

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  6. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  20. If lim(xrarr0)(axe^x-blog(1+x))/x^2=3 ,then the values of a ,b are res...

    Text Solution

    |