Home
Class 12
MATHS
f(x) ={{:(0, x=0),(x-3, x gt 0):} The ...

`f(x) ={{:(0, x=0),(x-3, x gt 0):}`
The function f(x) is:

A

increasing when `x ge 0`

B

strictly increasing when `x gt 0`

C

strictly increasing at `x=0`

D

not continuous at `x=0` and so it is not increasing when `x gt 0`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • QUESTION PAPER 2010

    WB JEE PREVIOUS YEAR PAPER|Exercise DESCRIPTIVE TYPE QEUSTIONS|10 Videos
  • QUESTION PAPER 2012

    WB JEE PREVIOUS YEAR PAPER|Exercise MULTIPLE CHOICE QUESTIONS|80 Videos

Similar Questions

Explore conceptually related problems

The function f(x)=|x|atx=0 is:

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

At x=0 the function f(x)=x^3+1 has -

Let g(x)=1+x-[x] and f(x)=={(-1, x lt0),(0, x=0),(1, x gt 0):} Then for all x find f(g(x))

If f(x)={(x"sin"(1)/(x),"when "x ne 0),(0,"when "x =0):} then at x = 0, the function f(x) is -

If f(x)={(x^3, x gt 0),(0, x=0),(-x^3, x lt0):}

Let f(x) be a polynomial of degree one and f(x) be a function defined by f(x)={(g(x), x le0), ((1+x)/(2+x)^(1//x), x gt0):} If f(x) is continuous at x=0 and f(-1)=f'(1), then g(x) is equal to :

Let f(x) be a function defined as f(x)= {(sin(x^2-3x),xle0),(6x+5x^2,xgt0):} Then at x=0,f(x)

Given f(0)=0 and f(x)=(1)/(1-e^(-(1)/(x))) for x ne 0 . Then the function f(x) is -

If f(x)={(-1, xlt0 ),(0, x =0),(1, x gt 0):} and g(x)=x(1-x^2), then , f(g(x)) is continuous for,

WB JEE PREVIOUS YEAR PAPER-QUESTION PAPER 2011-MULTIPLE CHOICE QUESTIONS
  1. int(pi)^(16pi) |sin x| dx=

    Text Solution

    |

  2. The degree and order of the differential equation y =x((dy)/(dx))^(2...

    Text Solution

    |

  3. f(x) ={{:(0, x=0),(x-3, x gt 0):} The function f(x) is:

    Text Solution

    |

  4. The function f(x) = ax + b is strictly increasing for all real x if

    Text Solution

    |

  5. int(cos 2x)/(cos x) dx=

    Text Solution

    |

  6. int (sin^(8)x - cos^(8)x)/(1-2sin^(2)x cos^(2)x) dx.

    Text Solution

    |

  7. The general solution of the differential equation log(e) ((dy)/(dx)) =...

    Text Solution

    |

  8. If y=A/x + Bx^(2), then x^(2) (d^(2)y)/(dx^(2)) =

    Text Solution

    |

  9. If one of the cube roots of 1 be omega, then |{:(1, 1+omega^(2), ome...

    Text Solution

    |

  10. 4 boys and 2 girls occupy seats in a row at random. Then the probabili...

    Text Solution

    |

  11. A coin is tossed again and again. If tail appears on first three tosse...

    Text Solution

    |

  12. The coefficient of x^(n) in the expansion of (e^(7x) + e^(x))/e^(3x) i...

    Text Solution

    |

  13. The sum of the series: 1/(1.2) -1/(2.3) +1/(3.4)-1/(4.5)………. infty i...

    Text Solution

    |

  14. The number (101)^(100)-1 is divisible by:

    Text Solution

    |

  15. If A and B are coefficients of x^(n) in the expansions of (1+x)^(2n) ...

    Text Solution

    |

  16. If n gt 1 is an integer and x ne 0 , then (1+x)^(n)-nx-1 is divisible...

    Text Solution

    |

  17. If ""^(n)C(4), ""^(n)C(5) and "'^(n)C(6) are in A.P., then n is:

    Text Solution

    |

  18. The number of diagonals in a polygon is 20. The number of sides of the...

    Text Solution

    |

  19. ""^(15)C(3) + ""^(15)C(5) + ……… +""^(15)C(15) =

    Text Solution

    |

  20. Let a, b, c be three real numbers such that a + 2b + 4c = 0. Then the ...

    Text Solution

    |