Home
Class 12
MATHS
f(x)={{:(|x|+3, if x le -3),(-2x, if -3 ...

`f(x)={{:(|x|+3, if x le -3),(-2x, if -3 lt x lt 3 ),(6x + 2, if x ge3):}`

Text Solution

AI Generated Solution

To solve the problem, we need to analyze the piecewise function \( f(x) \) defined as follows: \[ f(x) = \begin{cases} |x| + 3 & \text{if } x \leq -3 \\ -2x & \text{if } -3 < x < 3 \\ 6x + 2 & \text{if } x \geq 3 ...
Promotional Banner

Topper's Solved these Questions

  • Continuity and Differentiability

    NAGEEN PRAKASHAN|Exercise Exercies 5.2|10 Videos

  • Continuity and Differentiability

    NAGEEN PRAKASHAN|Exercise Exercies 5.3|15 Videos

  • Continuity and Differentiability

    NAGEEN PRAKASHAN|Exercise Exercies 5p|20 Videos

  • APPLICATIONS OF INTEGRALS

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|19 Videos

  • DETERMINANTS

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

f(x)={(|x|+3",","if", x le -3),(-2x",", "if", -3 lt x lt 3),(6x+2",","if",x ge 3):} is

Discuss the continuity of the function f, where f is defined by f(x){{:(3"," if 0 le x le 1),(4"," if 1lt x lt 3 ),(5"," if 3 le x le 10):}

Let f:R to R be a function defined as f(x)={{:(5,"if" x le 1),(a+bx , "if" 1 lt x lt 3),(b+5x , "if" 3 le x lt 5),(30 , "if" x ge 5):} then f is

If f(x)={:{(3", if " 0 le x le 1),(4", if " 1 lt x lt 3),(5", if " 3 le x le 10):} , then

Function f(x)={{:(2x-1", if "x le 1 ),(x^(2)", if "1 lt x ),(3x - 4 " , if " 2 lt x lt 4 ):} is continuous on

f(x)={{:(,[x]," if "-3 lt x le -1),(,[x]," if "-1 lt x lt),(,|[-x]|," if "1 le x lt 3):}" then "{x : f(x) ge 0} is equal to :

NAGEEN PRAKASHAN-Continuity and Differentiability-Exercies 5.1
  1. Is the function f defined by f(x)={{:(x, if x le 1),(5, if x gt 1):...

    Text Solution

    |

  2. f(x)=2x+3 if x<= 2 and f(x)=2x-3 if x > 2

    Text Solution

    |

  3. f(x)={{:(|x|+3, if x le -3),(-2x, if -3 lt x lt 3 ),(6x + 2, if x ge3)...

    Text Solution

    |

  4. {{:((|x|)/(x)","if x ne 0 ),(0"," if x = 0 ):}

    Text Solution

    |

  5. {{:((x)/(|x|)","if x lt 0 ),(-1"," if x ge 0 ):}

    Text Solution

    |

  6. f(x) {{:(x + 1"," if x ge 1 ),(x^(2)+ 1"," if x lt 1):}

    Text Solution

    |

  7. f(x){{:(x^(3) - 3"," if x le 2 ),(x^(2) + 1"," if x gt 2 ):}

    Text Solution

    |

  8. f(x){{:(10^(3) - 1"," if x le 1 ),(x^(2) "," if x gt 1 ):}

    Text Solution

    |

  9. Is the function defined by f(x)={x+5, ifxlt=1x-5, ifx >1 a continuous...

    Text Solution

    |

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

    Text Solution

    |

  11. f(x){{:(2x "," if x lt 0 ),(0"," if 0 le x le 1),(4x "," if x gt 1 ):}

    Text Solution

    |

  12. f(x) {{:(-2"," if x le -1),(2x"," if -1lt x le 1),(2"," if x gt 1):}

    Text Solution

    |

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

    Text Solution

    |

  14. For what value of lambdais the function defined by f(x)={lambda(x^2-2...

    Text Solution

    |

  15. Show that the function defined by g(x)=x-[x] is discontinuous at all i...

    Text Solution

    |

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

    Text Solution

    |

  17. Discuss the continuity of the following functions:(a) f(x) = s in x + ...

    Text Solution

    |

  18. Discuss the continuity of the cosine, cosecant, secant and cotangen...

    Text Solution

    |

  19. Find all points of discontinuity of f, wheref(x)={(sinx)/x , ifx<0x+1,...

    Text Solution

    |

  20. Determine if f defined byf(x)={x^2sin1/x , ifx!=0 0, ifx=0

    Text Solution

    |