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Math Help - Function notations/inverse functions.

  1. #1
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    Function notations/inverse functions.

    Hello,
    I can't solve this maths question and I would really appreciate your help.
    My problem is:

    Let f(x) =
    __ (this means "square root of x" - I didn't know how to type it!)
    V x

    and g(x) = 2^x. Solve the equation

    (f^-1 o g)(x) = 0.25.

    Thanks.
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by Aminekhadir View Post
    Hello,
    I can't solve this maths question and I would really appreciate your help.
    My problem is:

    Let f(x) =
    __ (this means "square root of x" - I didn't know how to type it!)
    V x

    and g(x) = 2^x. Solve the equation

    (f^-1 o g)(x) = 0.25.

    Thanks.
    f(x)=\sqrt{x}

    g(x)=2^x

    f^{-1}(x)\rightarrow x=\sqrt{y} \rightarrow y=x^2

    \left[f^{-1} \circ g\right](x)=(2^x)^2=2^{2x}

    2^{2x}=.25

    2^{2x}=\frac{1}{4}

    2^{2x}=\frac{1}{2^2}

    2^{2x}=2^{-2}

    2x=-2

    x=-1
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  3. #3
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    Quote Originally Posted by Aminekhadir View Post
    Hello,
    I can't solve this maths question and I would really appreciate your help.
    My problem is:

    Let f(x) =
    __ (this means "square root of x" - I didn't know how to type it!)
    V x

    and g(x) = 2^x. Solve the equation

    (f^-1 o g)(x) = 0.25.

    Thanks.
    f(x) = \sqrt{x}

    y = \sqrt{x}

    For f^{-1}(x), interchange, x and y and solve for y

    x = \sqrt{y}

    x^2=y

    y= x^2

    f^{-1}(x)=x^2\;\;\;\;and\;\;\;\;g(x)=2^x

    Now,

    (f^{-1}\;\;o\;\;g)(x)=(2^x)^2

    (2^x)^2=0.25

    2^{2x}=2^{-2}

    (because,\;\; 0.25=\frac{1}{4}=\frac{1}{2^2}=2^{-2})

    2x=-2

    x=-1

    did you get it now???
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  4. #4
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    Yes, thank you very much
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