Home
Class 12
MATHS
A function f (x) is defined as f(x)={{...

A function f (x) is defined as
`f(x)={{:(ax+2,"when "xle3),(bx+3,"when " xgt3):}`
If f (x) is continuous at x =3 then find the relation between a and b .

Text Solution

Verified by Experts

The correct Answer is:
`3(a-b)=2`
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    CHHAYA PUBLICATION|Exercise EXERCISE 2A ( Multiple Choice Type Questions)|2 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    CHHAYA PUBLICATION|Exercise EXERCISE 2A ( Very Short Answer Type Questions)|6 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    CHHAYA PUBLICATION|Exercise EXERCISE 2A ( short Answer Type Questions)|8 Videos

  • COMPLEX NUMBER

    CHHAYA PUBLICATION|Exercise SAMPLE QUESTION FOR COMPETITIVE EXAMS(Multiple Corrrect Answer type)|11 Videos

  • COORDINATE GEOMETRY

    CHHAYA PUBLICATION|Exercise JEE Advanced Archive (2016)|3 Videos

Similar Questions

Explore conceptually related problems

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.

A function f (x) is defined as followes: f(x)={{:(xsin.(1)/(x),"when " xne0),(0,"when " x=0):} Show that f (x) is continuous at x =0 .

A function f (x) is defined as follows: f(x)={{:(x^(4)-3,"when " xle2),(x^(3)+5,"when "xgt2):} Prove that the function f (x) is continuous at x = 2 .

If the function f(x)={{:((1-cos(ax))/(x^2)," when "xne0),(1," when "x=0):} be continuous at x=0, then find the value of a.

A function is defined as f(x) = {(e^x, xle0),(|x-1|, x gt0):} , then f(x) is

A function f (x) is defined as follows : f(x)={{:(2-x",","when "xlt1),(x^(2)-3x",","when "xge1):} Examine the differentiability of the function f (x) at x= 1 , hence state whether f (x) is continuous at x = 1 or not .

A function f (x) is defined as follwos : f(x){:(=2x+1," when "xle 1),(= 3-x," when "xgt1):} Examine whether underset(xrarr1)"lim"f(x) exists or not.

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 continuous function f(x) is defined as follows : f(x)={{:(x,"when "xlt1),(ax+bx^(2),"when "1lexle2),(2x^(2),"when "xgt2):} Find the values of a and b.

Let f(x)={{:((x^(3)+x^(2)-16x+20)/((x-2)^(2)),"when " xne2),(" "k,"when " x=2):} if f (x) is continuous for all x , find k.

CHHAYA PUBLICATION-CONTINUITY AND DIFFERENTIABILITY -EXERCISE 2A ( Long Answer Type Questions)
  1. Test the continuity of the function f (x) : f(x)={{:(x^(2)sin.(1)/(...

    Text Solution

    |

  2. A function f (x) is defined as follows : f(x)={{:(3x+1,"for "xle1 ),(...

    Text Solution

    |

  3. A function f (x) is defined as f(x)={{:(ax+2,"when "xle3),(bx+3,"whe...

    Text Solution

    |

  4. Let f(x)={{:((x^(3)+x^(2)-16x+20)/((x-2)^(2)),"when " xne2),(" "k,...

    Text Solution

    |

  5. Let f(x)={{:((1-cos2ax)/(xsin2x),"when " xne0),(" " (1)/(2),"when " ...

    Text Solution

    |

  6. If the following function f (x) is continuous at x = 0 , find k : ...

    Text Solution

    |

  7. The function f(x)=(x^(3)-1)/(x-1) is undefined at x = 1 . Redefine the...

    Text Solution

    |

  8. Show that the function f(x)={{:(x+(x+2)/(|x+2|),"when " xne-2),(" "-...

    Text Solution

    |

  9. If the function f(x)={{:(3ax+b,"for "xgt1),(" " 11,"when " x=1),(5...

    Text Solution

    |

  10. Let f(x)={{:((1-sin^(3)x)/(3cos^(2)x),"if "x lt(pi)/(2)),(a,"if "x=(pi...

    Text Solution

    |

  11. Let f(x)={{:((sin(a+1)x+sinx)/(x)",","when " xlt0),(" c,","wh...

    Text Solution

    |

  12. Show that the function f(x)=|sinx+cosx| is continuous at x = pi.

    Text Solution

    |

  13. Show that the function g(x)=x-[x] is discontinuous at all integral po...

    Text Solution

    |

  14. Find from the first principle , the derivatives of the following funct...

    Text Solution

    |

  15. Find from the first principle , the derivatives of the following funct...

    Text Solution

    |

  16. Find from the first principle , the derivatives of the following funct...

    Text Solution

    |

  17. Find from the first principle , the derivatives of the following funct...

    Text Solution

    |

  18. Find from the first principle , the derivatives of the following funct...

    Text Solution

    |

  19. Find from the first principle , the derivatives of the following funct...

    Text Solution

    |

  20. Find from the first principle , the derivatives of the following funct...

    Text Solution

    |