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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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 = ...
Originally Posted by math88 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 $\displaystyle 2=2x+\ln(x)~?$
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; Feb 17th 2014 at 07:05 AM.
Originally Posted by math88 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 $\displaystyle f^{-1}(2)$. Find the value of $\displaystyle a$ such that $\displaystyle f(a)=2~.$
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