Question

Evaluate the inverse of the function y=x^3+x.

Answer 1

solve for x

Answer 2

once you obtain x, replace x with y then you get your inverse function.

Answer 3

Is it easy to write x in terms of y? surely not...

Answer 4

\[y=x^3+x\]\[x=y^3+y\]\[0=y^3+y-x\] oh, that looks unappealing... :l

Answer 5

Cardan's method can be used here, but yields very unappealing answers...

Answer 6

can you use a calculator?

Answer 7

Let \(y=c\):\[
0 = x^3+x-c
\]Plug this into the equation for cubic functions to find generic answers in terms of \(c\).
\(f(c) = y^{-1}(x)\)

Answer 8

the cubic formula will give you 3 answers so you'll probably have to use test points to figure out which ones apply where.

It works, though it isn't elegant.