Home
Class 12
MATHS
Find the values of a and b so that the f...

Find the values of `a` and `b` so that the function `f` given by `f(x)={{:(a x+1, if xle3),(ax+3 , if x>3):}.`

Text Solution

Verified by Experts

Given function `f(x)={{:(a x+1, if xle3),(ax+3 , if x>3):}.`
Given function is continuous at `x=3`
`lim_(x->3^-) f(x) = lim_(x->3^+) f(x)`
`=>3a+1=3b+3`
`=>3a-3b=2`
`=>a-b=2/3`
Which is our required relation.
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL DISTRIBUTION

    RD SHARMA|Exercise Solved Examples And Exercises|141 Videos

  • DEFINITE INTEGRALS

    RD SHARMA|Exercise Solved Examples And Exercises|567 Videos

Similar Questions

Explore conceptually related problems

Find the values of a and b so that the function f given by f(x)={1, if xlt=3a x+b , if 3

Find the value of 'a' and 'b' such that the function defined by : f(x)={{:(5", if "xle2),(ax+b", if "2ltxlt5),(20", if "xge5):} is a continuous function.

Find the realtionship between a and b so that the function defined by f(x)={{:(,ax+1,x le 3),(,bx+3, x gt 3):}" is continuous at x=3"

Find the least value of a such that the function f given by f(x)=x^(2)+ax+1 is strictly increasing on (1,2)

Find the relationship between a and b so that the function f defined by: f(x)={a x+1b x+3 "if" x lt=3"if" x >3

Find the relationship between a and b so that the function 'f' defined by f(x)={a x+1,ifxlt=3b x+3,ifx<3 is continuous at x=3.

Find the relationship between a and b so that the function f defined by f(x)=ax+1, if x 3 is continuous at x=3.

Find the values of a and b so that the function f(x)={x^2+3x+a , bx2 ,ifxlt=1ifx >1 is differentiable at each xRdot

Find the values of a and b, if the function f(x) defined by f(x)={x^(2)+3x+a,x is differentiable at x=1

Find the maximum and minimum values , if any , of the function f given by f(x)=3-|x|

RD SHARMA-CONTINUITY-Solved Examples And Exercises
  1. If f(x)=(2x+3sinx)/(3x+2sinx),x!=0 is continuous at x=0 , then find f(...

    Text Solution

    |

  2. For what value of k is the function f(x)={(x^2-1)/(x-1)k, ,x!=1,x=1"...

    Text Solution

    |

  3. Find the values of a and b so that the function f given by f(x)={{:(a ...

    Text Solution

    |

  4. Let f(x)=(log(1+x/a)-log(1-x/b))/x ,\ \ x!=0 . Find the value of f at ...

    Text Solution

    |

  5. If f(x)={{:((cos^2x-sin^2x-1)/(sqrt(x^2+1)-1),if x ne 0),(k,if x=0):},...

    Text Solution

    |

  6. Extend the definition of the following by continuity f(x)=(1-cos7(x...

    Text Solution

    |

  7. Find the value of a for which the function f defined by f(x)={asinp...

    Text Solution

    |

  8. Show that f(x)={{:(1+x^2,if 0lt=xlt=1) ,(2-x, if x >1):} is discontin...

    Text Solution

    |

  9. {{:(x^(2)/2, if 0le x le 1),(2x^(2)-3x+3/2, if l lt x le 2):} at x = ...

    Text Solution

    |

  10. Examine the continuity of the function f(x)= {{:(3x-2,xlt=0),(x+1,x ...

    Text Solution

    |

  11. Discuss the continuity of the function f(x)={{:(x, x>0)(1, x=0)(-x , ...

    Text Solution

    |

  12. Discuss the continuity of the function f(x)={x/(|x|),x!=0 ,x=0

    Text Solution

    |

  13. If f(x)=(tan(pi/4-x))/(cot2x) for x!=pi/4, find the value which can be...

    Text Solution

    |

  14. Show that f(x)={{:(1+x^2,if 0lt=xlt=1) ,(2-x, if x >1):} is discontin...

    Text Solution

    |

  15. Show that f(x)={(x-|x|)/(2), w h e nx!=0 and 2 w h e nx=0 is disconti...

    Text Solution

    |

  16. Find the relationship between a and b so that the function 'f' def...

    Text Solution

    |

  17. If f(x)={(sin3x)/x,w h e nx!=0 1,w h e nx=0dot Find whether f(x) is co...

    Text Solution

    |

  18. Prove that the function f(x)={(sinx)/x,x<0,x+1,xgeq0 is everywhere ...

    Text Solution

    |

  19. Let f(x)={(1-cosx)/(x^2),\ \ \ w h e n\ x!=0 1,\ \ \ \ w h e n\ x=0 . ...

    Text Solution

    |

  20. If f(x)={e^(1/x) ,1 ifx!=0ifx=0 Find whether f is continuous a...

    Text Solution

    |