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Let f: (-1, 1) ->B be a function defi...

Let `f: (-1, 1) ->B` be a function defined by `f(x)=tan^-1 ((2x)/(1-x^2))` . Then f is both one-one and onto when B is the interval

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Let f:(-1,1)rarr B be a function defined by f(x)=tan^(-1)((2x)/(1-x^(2))). Then f is both one- one and onto when B is the interval

Let f:(-1,1)rarr B be a function defined by f(x)=tan^(-1)[(2x)/(1-x^(2))]. Then f is both one- one and onto when B is the interval.(a) [0,(pi)/(2))(b)(0,(pi)/(2))(c)(-(pi)/(2),(pi)/(2))(d)[-(pi)/(2),(pi)/(2)]

Knowledge Check

  • If f:(-1,1) to B be a function defined by f (x) = tan^(-1) (2x)/(1-x^2) , then f is both one-one and onto when B is the interval :

    A
    `[- (pi)/(2) ,(pi)/(2)]`
    B
    `(-(pi)/(2) ,(pi)/(2))`
    C
    `[0,(pi)/(2)]`
    D
    `[0,(pi)/(2))`

  • Let f:R rarr B be a functio defined by f(x)=tan^(-1).(2x)/(1+x^(2)) , then f is both one - one and onto when B is in the interval

    A
    `(0, (pi)/(4))`
    B
    `[0, (pi)/(3)]`
    C
    `[-(pi)/(4), (pi)/(4)]`
    D
    `(-(pi)/(4), (pi)/(4))`

  • Let f:R rarr B , be a function defined f(x)=tan^(-1).(2x)/(sqrt3(1+x^(2))) , then f is both one - one and onto when B, is the interval

    A
    `(0, (x)/(6))`
    B
    `[0, (pi)/(6))`
    C
    `[-(pi)/(6), (pi)/(6)]`
    D
    `(-(pi)/(6),(pi)/(6))`

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    Let f: R->R be a function defined by f(x)=(x^2-8)/(x^2+2) . Then, f is (a) one-one but not onto (b) one-one and onto (c) onto but not one-one (d) neither one-one nor onto

    Let f:[-1,1] rArr B be a function defined as f(x)=cot^(-1)(cot((2x)/(sqrt3(1+x^(2))))) . If f is both one - one and onto, then B is the interval

    Let f:R rarr [0, (pi)/(2)) be a function defined by f(x)=tan^(-1)(x^(2)+x+a) . If f is onto, then a is equal to

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