Home
Class 12
MATHS
Draw the graph of f(x) ={2x}, where {*} ...

Draw the graph of `f(x) ={2x}`, where `{*}` represents the fractional part function.

Text Solution

Verified by Experts

We have `f(x) = {2x}=2x- [2x]`
`" "={{:(......,,), (......,,),(2x+1",",,2x in [-1, 0) or x in [-1//2, 0)),(2x",",, 2x in [0, 1) or x in [0, 1//2)), (2x-1",",,2x in [1, 2) or x in [1//2, 1)), (2x-2",",, 2x in [2, 3) or x in [ 1, 3//2)),(2x-3",",,2x in [3, 4) or x in [3//2, 2)), (......,,),(......,,):}`
Thus, the graph is as shown in the following figure.
Promotional Banner

Topper's Solved these Questions

  • GRAPHS OF ELEMENTARY FUNCTIONS

    CENGAGE|Exercise Exercise|34 Videos
  • GRAPHS OF POLYNOMIAL AND RATIONAL FUNCTIONS

    CENGAGE|Exercise Exercise|13 Videos
  • GRAPHS OF TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise|22 Videos

Similar Questions

Explore conceptually related problems

Draw the graph of f(x) = {sin x}, where {*} represents the fractional part function.

Draw the graph of y^(2)= {x} , where {*} represents the fractional part function.

Draw the graph of y= 2^({x}) , where {*} represents the fractional part function.

Draw the graph of y=|{x}-0.5| , where {.} represents the fractional part function.

Draw the graph of y={|x|} , where {.} represents the fractional part function.

Draw the graph of |y|={x} , where {.} represents the fractional part function.

Draw the graphs of y=sin^(-1){x}," where "{*} resresent the fractional part function.

Draw the graph of y= {x}^(2) , where [*] represents the fractional part function.

Solve : x^(2) = {x} , where {x} represents the fractional part function.

CENGAGE-GRAPHS OF ELEMENTARY FUNCTIONS -Exercise
  1. Draw the graph of f(x) ={2x}, where {*} represents the fractional part...

    Text Solution

    |

  2. Draw the graph of y= (1)/((1//x)).

    Text Solution

    |

  3. (a) Draw the graph of f(x) = ={{:(1",",, |x| ge 1), ((1)/(n^(2)) ",",,...

    Text Solution

    |

  4. Sketch the regions which points satisfy |x+y| ge 2.

    Text Solution

    |

  5. Sketch the region satisfying |x| lt |y|.

    Text Solution

    |

  6. For a point P in the plane, let d1(P)a n dd2(P) be the distances of th...

    Text Solution

    |

  7. Draw the graph of y= (x-1)/(x-2).

    Text Solution

    |

  8. The following figure shows the graph of f(x) =ax^(2)+bx +c, then find ...

    Text Solution

    |

  9. The entire graph of the equation y=x^2+k x-x+9 in strictly above the x...

    Text Solution

    |

  10. If x^2+2a x+a<0AAx in [1,2], the find the values of adot

    Text Solution

    |

  11. Draw the graph of f(x) = x|x|.

    Text Solution

    |

  12. Draw the graph of the function: Solve |(x^2)/(x-1)|lt=1 using the grap...

    Text Solution

    |

  13. Draw the graph of y = |x^(2) - 2x|-x.

    Text Solution

    |

  14. Draw the graph of y = {{:(2^(x)",",, x^(2)-2x le 0 ),( 1+3.5 x- x^(2),...

    Text Solution

    |

  15. Draw the graph of f(x) = |x-1|+ |2x-3|. Find the range of the functio...

    Text Solution

    |

  16. Draw the graph of y= |x-1|+3|x-2|-5|x-4| and find the values of lamda ...

    Text Solution

    |

  17. Find the set of real value(s) of a for which the equation |2x+3|+2x-3|...

    Text Solution

    |

  18. Draw the graph of y= 2^(((|x|+x))/(x)).

    Text Solution

    |

  19. Draw the graph of y= x ^((1)/(log(e)x)).

    Text Solution

    |

  20. Find the number of solutions to the question x+log(e)x=0.

    Text Solution

    |

  21. draw the graph of f(x)=x+[x], [.] denotes greatest integer function.

    Text Solution

    |