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Let f: [-pi/2, pi/2]rarr[-1, 1], where f...

Let `f: [-pi/2, pi/2]rarr[-1, 1]`, where f(x)=sinx. Find whether f(x) is one-one or not.

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Knowledge Check

  • Let f:[-pi/3, 2pi/3] rarr [0,4] be a function defined as f(x)=sqrt3 sinx-cosx+2 . Then f^-1(x) is given by

    A
    `sin^-1(x-2/2)-pi/6`
    B
    `sin^-1((x-2)/2)+pi/6`
    C
    `2pi/3-cos^-1((x-2)/2)`
    D
    none of these

  • Let f : (-infty,1] rarr (-infty, 1] such that f(x) = x(2 -x), then f^-1 (x) is

    A
    `1 + sqrt(1 -x)`
    B
    `1 - sqrt(1 -x)`
    C
    `sqrt(1 -x)`
    D
    ` sqrt(1 +x)`

  • If f : R to [-1, 1] , where f(x)=sin(pi/2[x]) (where [.] denotes the greatest integer function), then the range of f(x) is

    A
    [-1, 1]
    B
    {-1, 1}
    C
    {-1, 0, 1}
    D
    None of these

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    Assertion Let f:R→R , f(x) = x^3+x^2+3x+sinx f(x) is one-one. Reason f(x) is decreasing function.

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