Inverse function help

[mr_pj]

If f(x) = 2x + ln x, find f-1(2) <- the inverse function of f(x)

How do I solve this?

 

[tkhunny]

If f(x) = 2x + ln x, find f-1(2) <- the inverse function of f(x)

You're a little bit out of luck if you are looking for a closed-form solution containign only elementary functions. The presence of 'x' inside of and outside of the logarithm is not reconcilable. You must seek numeric solutions and hope for the best.

Fortunately, f(1) = 2, so f^-1(2) = 1, but it was only by luck that I stumbled over that.

(Really, I was just poking around. I was going to try f(1) and f(2), just to see where the solution was. It was only by accident that I tripped over it exactly.)