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Math Help - The inverse of f(x)

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    The inverse of f(x)

    Hi everyone, I really don't know how to solve this problem. Please help me or give me some ideas to solve it. Thank you very much.

    Given f(x) = 2x + ln x. Suppose f(x) has the inverse f^-1(x) on D=[1,infinity). Find f^-1(2)
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    Re: The inverse of f(x)

    First of all, is the function one to one on the domain given? This is necessary to ensure that the inverse is a function.

    Then to find the inverse, swap the x and y and solve to get y = ...
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    Re: The inverse of f(x)

    Quote Originally Posted by math88 View Post
    Hi everyone, I really don't know how to solve this problem. Please help me or give me some ideas to solve it. Given f(x) = 2x + ln x. Suppose f(x) has the inverse f^-1(x) on D=[1,infinity). Find f^-1(2)
    Can you solve 2=2x+\ln(x)~?
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    Re: The inverse of f(x)

    I don't understand why f(x)=2=2x+ln(x)
    I can't find the inverse of f(x) because I can't solve for x (x=g(y)).
    Last edited by math88; February 17th 2014 at 07:05 AM.
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    Re: The inverse of f(x)

    Quote Originally Posted by math88 View Post
    I don't understand why f(x)=2=2x+ln(x)
    I can't find the inverse of f(x) because I can't solve for x (x=g(y)).
    The question does not ask you to find the inverse function. You don't need that.

    The question asks you to find the value of f^{-1}(2).
    Find the value of a such that f(a)=2~.
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