Home
Class 12
MATHS
Is the function f defined by {{:(x," i...

Is the function f defined by
`{{:(x," if "x le 1),(5," if "x gt 1):}`
continuous at x= 0? At x=1? At x=2?.

Text Solution

Verified by Experts

The correct Answer is:
f is continuous at x=0 and x=2; not continuous at x=1.
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    NCERT TAMIL|Exercise EXERCISE 5.2|10 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    NCERT TAMIL|Exercise EXERCISE 5.3|15 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    NCERT TAMIL|Exercise MISCELLANEOUS EXAMPLES|9 Videos

  • COMPLEX NUMBERS

    NCERT TAMIL|Exercise EXERCISE 2.9|25 Videos

  • DETERMINANTS

    NCERT TAMIL|Exercise Miscellaneous Exercises on Chapter 4|19 Videos

Similar Questions

Explore conceptually related problems

Is the function defined by f(x)={{:(x+5," if "x le1),(x-5," if "x gt 1):} a continuous function?

Find the relationship between a and b so that the function f defined by f(x)={{:(ax+1-2," if "x le 3),(bx+3," if "x gt 3):} is continuous at x=3.

For what value of lambda is the function defined by f(x)={{:(lambda(x^(2)-2x)," if "x le 0),(4x+1," if "x gt 0):} continuous at x= 0? What about continuity at x =1?

Discuss the continuity of the function f defined by {{:(x+2," if "x le 1),(x-2," if "x gt 1):} .

Find all the points of discontinuity of the function f defined by {{:(x+2," if "x lt 1),(0," if "x=1),(x-2," if "x gt 1):} .

Discuss the continuity of the function defined by {{:(x+2," if "x lt 0),(-x+2," if "x gt 0):}

Discuss the continuity of the function f, where f is defined by f(x)={{:(-2," if "x le -1),(2x," if "-1 lt x le 1),(2," if "x gt 1):} .

Discuss the continuity of the function f, where f is defined by f(x)={{:(2x," if "x lt 0),(0," if "0 le x le 1),(4x," if "x ge 1):} .

Find the values of k so that the function f is continuous at the indicated point. f(x)={{:(kx+1," if "x le 5),(3x-5," if "x gt 5):}" at "x= 5 .

NCERT TAMIL-CONTINUITY AND DIFFERENTIABILITY-EXERCISE 5.1
  1. Examin the following functions for continuity. f(x)= |x-5|.

    Text Solution

    |

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

    Text Solution

    |

  3. Is the function f defined by {{:(x," if "x le 1),(5," if "x gt 1):} ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  9. Find the points of discontinuity of the function f, where f(x)={{:(x...

    Text Solution

    |

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

    Text Solution

    |

  11. Is the function defined by f(x)={{:(x+5," if "x le1),(x-5," if "x gt...

    Text Solution

    |

  12. Discuss the continuity of the function f, where f is defined by f(x)...

    Text Solution

    |

  13. Discuss the continuity of the function f, where f is defined by f(x)...

    Text Solution

    |

  14. Discuss the continuity of the function f, where f is defined by f(x)...

    Text Solution

    |

  15. Find the relationship between a and b so that the function f defined b...

    Text Solution

    |

  16. For what value of lambda is the function defined by f(x)={{:(lambda(...

    Text Solution

    |

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

    Text Solution

    |

  18. Is the function defined by f(x)= x^(2)-sin x+5 continuous at x= pi?

    Text Solution

    |

  19. Discuss the continuity of the following functions : f(x)= sin x +cos...

    Text Solution

    |

  20. Discuss the continuity of the following functions : f(x)= sin x - co...

    Text Solution

    |