The inverse of f(x)

• Feb 17th 2014, 05:40 AM
math88
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)
• Feb 17th 2014, 05:49 AM
Prove It
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 = ...
• Feb 17th 2014, 06:09 AM
Plato
Re: The inverse of f(x)
Quote:

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 $\displaystyle 2=2x+\ln(x)~?$
• Feb 17th 2014, 07:01 AM
math88
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)).
• Feb 17th 2014, 07:14 AM
Plato
Re: The inverse of f(x)
Quote:

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 $\displaystyle f(a)=2~.$