Home
Class 12
MATHS
Write the equivalent (piecewise) definit...

Write the equivalent (piecewise) definition of `f(x)=sgn(sinx)dot`

Text Solution

Verified by Experts

`f(x) = sgn (sin x) = {{:(-1",", sin x lt 0),(0",", sin x = 0),(1",", sin x gt 0):}`
` = {{:(-1",", x in ((2n + 1) pi"," (2n + 2)pi)),(0",", x = npi"," n in Z),(1",", x in ((2npi)","(2n + 1)pi)):}`
Promotional Banner

Topper's Solved these Questions

  • GRAPHS OF TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise|22 Videos

  • GRAPHS OF ELEMENTARY FUNCTIONS

    CENGAGE|Exercise Exercise|34 Videos

  • HIGHT AND DISTANCE

    CENGAGE|Exercise JEE Previous Year|3 Videos

Similar Questions

Explore conceptually related problems

Write the equivalent (piecewise) definition of f(x)=sgn(sin x)

The equivalent definition of f(x)=||x|-1| , is

Draw the graph of the function f(x)=max.{sin x,cus2x},x in[0,2 pi] Write the equivalent definition of f(x) and find the range of the function.

Write five equivalent fractions of 3/5dot

Find the equivalent definition of f(x)=max{x^(2),(1-x)^(2),2x(1-x)} where 0<=x<=1

If f(x)=x^(3)sgn(x), then

What is the equivalent definition of the function given by {:f(x)={(2x",",xge0),(0",",lt0):}

CENGAGE-GRAPHS OF TRIGONOMETRIC FUNCTIONS-Exercise
  1. Write the equivalent (piecewise) definition of f(x)=sgn(sinx)dot

    Text Solution

    |

  2. Draw the graph of y = " cosec "^(2) x - cot^(2) x. Is f(x) periodic ? ...

    Text Solution

    |

  3. Draw the graph of y = cos pix.

    Text Solution

    |

  4. Draw the graph of y = cos^(2)x.

    Text Solution

    |

  5. Find the values of x for which f(x) = sqrt(sin x - cos x) is defined.

    Text Solution

    |

  6. Draw the graph of y = tan^(2) x.

    Text Solution

    |

  7. Draw the graph of y = sin x + cos x, x in [0, 2pi].

    Text Solution

    |

  8. Draw the graph of y = [cos x], x in [0, 2pi], where [*] represents the...

    Text Solution

    |

  9. Draw the graph of y = sin pisqrt(x).

    Text Solution

    |

  10. Find the number of roots of the equation x sin x = 1, x in [-2pi, 0) ...

    Text Solution

    |

  11. Evaluate : [lim(x to 0) (tan x)/(x)], where [*] represents the greates...

    Text Solution

    |

  12. For f(x) = sin x - x^(2) + 1, check weather the function is increasing...

    Text Solution

    |

  13. Draw the graph of the function f(x)=m a xdot{sinx ,cos2x},x in [0,2pi]...

    Text Solution

    |

  14. Draw the graph of [y] = cos x, x in [0, 2pi], where [*] denotes the g...

    Text Solution

    |

  15. The total number of solution of sin {x}= cos {x} (where {.} denotes th...

    Text Solution

    |

  16. Draw the graph of f(x) = |tan x| + |cot x|.

    Text Solution

    |

  17. Find the number of solutions to cos x = (x)/(10), x gt 0.

    Text Solution

    |

  18. The number of solutions of tanx-m x=0,m >1, in (-pi/2,pi/2) is 1 (b) 2...

    Text Solution

    |

  19. Find the number of solutions to log(e) |sin x| = -x^(2) + 2x in [-(pi)...

    Text Solution

    |

  20. Solve :cos x le - (1)/(2).

    Text Solution

    |

  21. Prove that the least positive value of x , satisfying tanx=x+1, lies i...

    Text Solution

    |