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Math Help - Functions and their graphs

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    Functions and their graphs

    Find its inverse. State the domain and the range of f and f^-1. Graph f, f^-1, and y=x on the same coordinate axes.

    f (x)= (x^3) + 1
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    Quote Originally Posted by kukid123 View Post
    Find its inverse. State the domain and the range of f and f^-1. Graph f, f^-1, and y=x on the same coordinate axes.

    f (x)= (x^3) + 1
    Unless otherwise stated, the domain of any polynomial is always \mathbf{R}.

    It always helps to sketch the graph to start with.

    So the domain of f(x) = x^3 + 1 is \mathbf{R}.

    It's range is also \mathbf{R}.



    To find the inverse, your x and y (or in this case, f) values swap, and so do the domain and range.

    Since the domain and range of f were both \mathbf{R}, so are the domain and range of f^{-1}.

    Now we just find what the inverse function is.

    x = y^3 + 1

    x - 1 = y^3

    y = \sqrt[3]{x - 1}

    f^{-1}(x) = \sqrt[3]{x - 1}.

    Now graph this function.
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