Let f(x) = 3x + 1/ x + 5, for x ≠ 1. Find f⁻¹(x).

Answer 1

Hi Ady R.,

Something is wrong in your transcription of the problem, perhaps. There is no reason to limit x .notequalto. 1, but there is for x .notequalto. 0. (namely, a domain exclusion due to the 1/x term)

Note that there is no trivial way of solving for y=f(x), because of the x^1 and x^(-1) terms together.

But there is an even worse problem: since the function f(x) is not monotonically ascending, there will be (for many values of f(x) ) two values which map via f^(-1)(x) onto x. That's not a function!

So "does not exist" would be a reasonable answer.

--Cheers, --Mr. d.