Home
Class 12
MATHS
Prove that the identity function on real...

Prove that the identity function on real numbers given by `f(x)= x` is continuous at every real number

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF INTEGRALS

    V PUBLICATION|Exercise QUESTION BANK|45 Videos

  • DETERMINANT

    V PUBLICATION|Exercise QUESTION BANK|136 Videos

Similar Questions

Explore conceptually related problems

Prove that the function f is given by f(x)=|x-1| , x in R is not differentiable at x=1

Prove that the function f: Q rarr Q given by f(x)=2 x-3 for all x in Q (the set of all rational numbers) is a bijection.

Prove that every rational function is continuous.

Prove that the function defined by f(x)= cosx^2 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)=2x-5 is continuous at x=-2

Discuss the continuity of the function f is given by f(x)=|x| at x=0

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

Prove that the function f(x)=x^n is continuous at x=n, where n is a positive integer.

Solve 4x-5<7 , when x is a real number.

V PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. Show that the function f(x)={(x^3+3ifxne0),(1ifx=0):} is not continuou...

    Text Solution

    |

  2. Check the point where the constant function f(x)=k is continuous.

    Text Solution

    |

  3. Prove that the identity function on real numbers given by f(x)= x is c...

    Text Solution

    |

  4. Discuss the continuity of the function f is given by f(x)=|x| at x=0

    Text Solution

    |

  5. Discuss the continuity of the function f(x)=x^3+x^2-1

    Text Solution

    |

  6. Discuss the continuity of the function f(x)=1/x,xne0

    Text Solution

    |

  7. Check the continuity of the function f(x)={(x,+,2,if,x,<,0),(-x,+,2,...

    Text Solution

    |

  8. Discuss the continuity of the function given by f(x)={(x, if, x ...

    Text Solution

    |

  9. Show that every polynomial function is continuous

    Text Solution

    |

  10. Prove that the greatest integer function f : R rarrR given by f(x) =[x...

    Text Solution

    |

  11. Prove that every rational function is continuous.

    Text Solution

    |

  12. Discuss the continuity of sine function.

    Text Solution

    |

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

    Text Solution

    |

  14. Prove that the function f(x)=5x-3 is continuous at x=0, at x=-3 and at...

    Text Solution

    |

  15. Examine the continuity of the function f(x)=2x^2-1 at x=3

    Text Solution

    |

  16. Examine the following functions for continuity f(x)=1/(x-5)

    Text Solution

    |

  17. Prove that the function f(x)=x^n is continuous at x=n, where n is a p...

    Text Solution

    |

  18. Is the function f defined by f(x)={(x","ifxle1),(5"," ifx>1):} continu...

    Text Solution

    |

  19. Find all points of discontinuity of f where f is defined by f(x)={(2x+...

    Text Solution

    |

  20. Find all points of discontinuity of f, where f is defined by f(x)={(|...

    Text Solution

    |