Home
Class 12
MATHS
If f: RtoS , defined by f(x)=sinx-sqrt(3...

If `f: RtoS ,` defined by `f(x)=sinx-sqrt(3)cosx+1,is onto ,` then find the set `Sdot`

Text Solution

Verified by Experts

The correct Answer is:
[-1, 3]
`f(x)=sinx-sqrt(3)cosx+1`
`=2("sin"x(1)/(2)-"cos"(sqrt(3))/(2))+1`
`=2(sinx"cos"(pi)/(3)-cosx"sin"(pi)/(3))+1`
`=2"sin"(x-(pi)/(3))+1`
Clearly, `f` is onto, when the interval of S is `[-1,3].`
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

If f:R to S is defined by f(x)=sinx-sqrt(3)cosx+1 is onto, then the interval of S is -

Let a function f:R to R be defined by f(x)=2x+cosx+sinx " for " x in R . Then find the nature of f(x) .

Let f:XtoY be a function defined by f(x)=asin(x+pi/4)+bcosx+c . If f is both one-one and onto, find sets X and Y.

Let the function f: RrarrR be defined by f(x)=2x+sinx for x in Rdot Then f is (a)one-to-one and onto (b)one-to-one but not onto (c)onto but not-one-to-one (d)neither one-to-one nor onto

Let D be the set of odd natural numbers . Then show that the mapping f:NN rarrD , defined by, f(x)=2x-3 is onto but the mapping g:ZZ rarrZZ defined by , g(x)=2x-3 is not onto.

Let A=RR - {3} and B =RR-{1} . Prove that the function f: A rarr B defined by , f(x)=(x-2)/(x-3) is one-one and onto. Find a formula that defines f^(-1)

The domain of f(x)=1/(sqrt(|cosx|+cosx)) is

If two real functions f and g are defined respectively by f(x)=sqrt(x+1) and g(x)=sqrt(x-1), then the find the values of (f)/(g)(1) and (g)/(f)(1). Also find the domain of definitions of (f)/(g) and (g)/(f).

If [2sinx]+[cosx]=-3 then the range of the function f(x)=sinx+sqrt3cosx in [0, 2pi] is, (where [.] denotes the greatest integer function)

The function f(x)=(sinx)/(sinx-cosx) is discontinuous at -

CENGAGE PUBLICATION-RELATIONS AND FUNCTIONS-All Questions
  1. A function f from the set of natural numbers to the set of integers ...

    Text Solution

    |

  2. If f: R to R is given by f(x)=(x^2-4)/(x^2+1) , identify the type of f...

    Text Solution

    |

  3. If f: RtoS , defined by f(x)=sinx-sqrt(3)cosx+1,is onto , then find t...

    Text Solution

    |

  4. Let g: Rvec(0,pi/3) be defined by g(x)=cos^(-1)((x^2-k)/(1+x^2)) . The...

    Text Solution

    |

  5. Identify the type of the function f:R to R, f(x)=e^(x^(2))+cosx.

    Text Solution

    |

  6. Let a function f:R to R be defined by f(x)=2x+cosx+sinx " for " x in ...

    Text Solution

    |

  7. If f:R to R given by f(x)=x^(3)+px^(2)+qx+r, is then find the conditi...

    Text Solution

    |

  8. The entire graphs of the equation y=x^2+kx-x+9 is strictly above the x...

    Text Solution

    |

  9. Find the range of f(x)=(x^2+34 x-71)/(x^3+2x-7)

    Text Solution

    |

  10. Find the range of f(x)=sqrt(x-1)+sqrt(5-x)

    Text Solution

    |

  11. If f(x)=sqrt(x^2+a x+4) is defined for all x , then find the value of ...

    Text Solution

    |

  12. Find the domain and range of f(x)=sqrt(3-2x-x^2)

    Text Solution

    |

  13. Find the domain of f(x)=sqrt(sinx)+sqrt(16-x^2)

    Text Solution

    |

  14. Solve sinx > -1/2

    Text Solution

    |

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

    Text Solution

    |

  16. Find the range of f(x)=sec(pi/4cos^2x)

    Text Solution

    |

  17. If x in [1,2] , then find the range of f(x)=tanx

    Text Solution

    |

  18. Find the range of f(x)=1/(1-3sqrt(1-sin^2x))

    Text Solution

    |

  19. Find the range of f(x)=(2sin^2x+2sinx+3)/(sin^2x+sinx+1)

    Text Solution

    |

  20. Draw the graph of y=(sin2x)sqrt(1+tan^2x) , find its domain and range.

    Text Solution

    |