What is the inverse of the function f(x) = 3x + ln x?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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We have to find the inverse function of f(x) = 3x + ln x

Let y = f(x) = 3x + ln x

Now, we have to express x in terms of y to determine the inverse function.

Here, y = 3x + ln x; it can be seen that we can neither bring x from the first term inside the ln function nor can we take the x from the ln function outside. Also, there is no corresponding value for y for values of x <= 0. This makes it impossible to express x in terms of y.

It is not possible to find the inverse function of f(x) = 3x + ln x

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fleetadmiral | High School Teacher | eNotes Newbie

Posted on

You can find the inverse function of f(x) = 3x +lnx. The process requires the use of the Lambert W-function. The inverse function is (1/3)W(3e^x). 

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