Home
Class 12
MATHS
Show that the function f defined by f(x)...

Show that the function `f` defined by `f(x)=|1-x+|x||` is everywhere continuous.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL DISTRIBUTION

    RD SHARMA ENGLISH|Exercise All Questions|149 Videos
  • DEFINITE INTEGRALS

    RD SHARMA ENGLISH|Exercise All Questions|562 Videos

Similar Questions

Explore conceptually related problems

Show that the function f defined by f(x)=|1-x+x|, where x is any real number, is a continuous function.

Show that the function f:NtoN defined by f(x)=2x-1 is one-one but not onto.

Show that the function defined by f(x) = | cos x | is a continuous function.

Show that the function defined by f(x) = sin(x^2) is a continuous function.

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

Show that the function defined by f(x)=cos(x^2) is a continuous function.

Prove that the function defined by f(x) = t a n x is a continuous function.

Show that the function f defined as follows f(x)={3x-2, 0 2 is continuous at x=2 , but not differentiable thereat.

Show that the function f: Q->Q defined by f(x)=3x+5 is invertible. Also, find f^(-1) .

Domain of the function f defined by f(x) = sqrt(x-1) is given by

RD SHARMA ENGLISH-CONTINUITY-All Questions
  1. Discuss the continuity of the function f(x)={(|x|)/x\ \ \ ,\ \ \ if...

    Text Solution

    |

  2. Discuss the continuity of the function f(x) given by f(x)={2x-1,ifx<0...

    Text Solution

    |

  3. Show that the function f defined by f(x)=|1-x+|x|| is everywhere co...

    Text Solution

    |

  4. Prove that f(x)=sqrt(|x|-x) is continuous for all xgeq0 .

    Text Solution

    |

  5. Given f(x)=1/(x-1) . Find the points of discontinuity of the compos...

    Text Solution

    |

  6. Determine the value of the constant k so that the function f(x)={k ...

    Text Solution

    |

  7. Determine the value of the constant m so that the function f(x)={m(x...

    Text Solution

    |

  8. If f(x)={3ax+b if x>1, 11 if x=1 , 5ax-2b,if x<1.Determinethe values o...

    Text Solution

    |

  9. Prove that the function f(x)={(sinx)/x\ \ \ ,\ \ \ x<0\ \ \ \ \x+1\ ...

    Text Solution

    |

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

    Text Solution

    |

  11. Find the points of discontinuity, if any, of the following function:...

    Text Solution

    |

  12. Find the points of discontinuity, if any, of the following function:...

    Text Solution

    |

  13. Find the points of discontinuity, if any, of the following function...

    Text Solution

    |

  14. Find the points of discontinuity, if any, of the following function...

    Text Solution

    |

  15. Find the points of discontinuity, if any, of the following function:...

    Text Solution

    |

  16. Find the points of discontinuity, if any, of the following function:...

    Text Solution

    |

  17. Find the points of discontinuity, if any, of the following function:...

    Text Solution

    |

  18. Find the points of discontinuity, if any, of the following function...

    Text Solution

    |

  19. Find the points of discontinuity, if any, of the following function:...

    Text Solution

    |

  20. Find the points of discontinuity, if any, of the following function...

    Text Solution

    |