Home
Class 12
MATHS
Find the period of the following functi...

Find the period of the following functions
(i) ` f(x)=|sin 3x|`
(ii) `f(x)=2"cosec"(5x-6)+7`
(iii) ` f(x) =x-[x-2.6],` where [.] represents the greatest integer function.

Text Solution

Verified by Experts

(i) Period of ` |sinx| " is " pi`.
So, the period of `|sin 3x| " is " (pi)/(3)`
(ii) Period of `2 "cosec"(5x-6)+7 " is " (2pi)/(5)`
(iii) `f(x) =x-[x-2.6]`
`=(x-2.6)-[x-2.6]+2.6`
`={x-2.6}+2.6,` where {.} represents fractional part function.
` :. ` Period of f(x) is '1'.
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|3 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE PUBLICATION|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

f:(2,3)->(0,1) defined by f(x)=x-[x] ,where [dot] represents the greatest integer function.

Find the period of following function f(x)=[sin3x]+[cos6x]

Find the range of the following function f(x)=sin^2x-5sinx-6

If f(x)= [sin^2x] (where [.] denotes the greatest integer function ) then :

Draw a graph of f(x) = sin {x} , where {x} represents the greatest integer function.

Draw the graph of f(x)=[tan^(-1)x]," where "[*]" represents the greatest integer function".

Find the renge of each of the following functions: f(x)=(x^2-5x+6)

Find the domain and range of f(x)="sin"^(-1)(x-[x]), where [.] represents the greatest integer function.

Period of f(x)=[x]+[x+1/3]+[x+2/3]-3x+10, where [.] denotes the greatest integer function.

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

CENGAGE PUBLICATION-RELATIONS AND FUNCTIONS-All Questions
  1. Verify that the period of function f(x) =sin^(10)x " is " pi.

    Text Solution

    |

  2. Prove that function f(x)=cos sqrt(x) is non-periodic.

    Text Solution

    |

  3. Find the period of the following functions (i) f(x)=|sin 3x| (ii...

    Text Solution

    |

  4. The fundamental period of the function f(x)=4cos^4((x-pi)/(4pi^2))-2co...

    Text Solution

    |

  5. Find the period of the following. (i) f(x)=(2^(x))/(2^([x])), where ...

    Text Solution

    |

  6. Discuss whether the function f(x)="sin"(cosx+x) is period or not. If y...

    Text Solution

    |

  7. In each of the following cases find the period of the function if it i...

    Text Solution

    |

  8. Find the period of (i) f(x)=sin pi x +{x//3}, where {.} represents ...

    Text Solution

    |

  9. Find the period f(x)=sinx+{x}, where {x} is the fractional part of xdo...

    Text Solution

    |

  10. If f(x)=sinx+cosa x is a periodic function, show that a is a rational ...

    Text Solution

    |

  11. Find the period of the following function (i) f(x) =|sinx|+|cosx| ...

    Text Solution

    |

  12. Let f:R→R: f(x)=x+1 and g:R→R: g(x)=2x−3. Find (f−g)(x).

    Text Solution

    |

  13. If f(x)=2^x the f(x+3)/ f(x-1)=?

    Text Solution

    |

  14. Let f:N→R such that f(x)=(2x−1)/2 and g:Q→R such that g(x)=x+2 be ...

    Text Solution

    |

  15. Suppose that g(x)=1+sqrt(x) " and " f(g(x))=3+2sqrt(x)+x. Then find th...

    Text Solution

    |

  16. The function f(x) is defined in [0,1] . Find the domain of f(t a nx)do...

    Text Solution

    |

  17. f(x)=x+1, x<0, f(x)=x^2, xgeq0 and g(x)={x^3, x<1, 2x-1, xgeq1 Then...

    Text Solution

    |

  18. find fog(x) " and " gof(x). if f(x)=x^2 and g(x)=cosx.

    Text Solution

    |

  19. Two functions are defined as under, f(x)={(x+1, x le1),(2x+1, 1ltxle2)...

    Text Solution

    |

  20. If f and g are one-one functions, then (a)f+g is one one (b)fg is one ...

    Text Solution

    |