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Find the inverse of the function: f:(-o...

Find the inverse of the function: `f:(-oo,1] rarr [1/2,oo],w h e r ef(x)=2^(x(x-2))`

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Knowledge Check

  • The function f:(-oo, 1] rarr (0, e^(5)] defined as f(x)=e^(x^(3)+2) is

    A
    Many one and onto
    B
    Many one and into
    C
    one - one and onto
    D
    one - one and into

  • The function f : (0, oo) rarr [0, oo), f(x) = (x)/(1+x) is

    A
    One-one and onto
    B
    One-one but not onto
    C
    Onto but not one-one
    D
    Neither one-one nor onto

  • If the function f:[1,oo)to[1,oo) is defined by f(x)=2^(x(x-1)) then f^(-1) is

    A
    `(1//2)^(x(x-1))`
    B
    `1/2(1+sqrt(1+4log_(2)x))`
    C
    `1/2(1-sqrt(1+rlog_(2)x))`
    D
    Not defined

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    The function f:R^(+)rarr(1,e) defined by f(x)=(x^(2)+e)/(x^(2)+1) is

    If the function f:[1,oo)to[1,oo) is defined by f(x)=2^(x(x-1)) , then f^(-1)(x) is

    Function f :(-oo, -1] to (0, e^(5)] defined by f(x)=e^(x^(3)-3x+2) is

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