Find f^-1(4) of f(x) = x^9 + x^3 + x + 1

Question

Find f^-1(4) of f(x) = x⁹ + x³ + x + 1

The only way I know how to do this is by using a graphing calculator. I don't know how to solve it by hand though. If anyone knows what I should do, please let me know. It would be greatly appreciated.

Answer 1

f(x) = x⁹ + x³ + x + 1

f(1) = 4. So, f^-1(4) = 1.

Answer 2

You might just stop where you are and not worry about isolating y. Say that your inverse function is implicitly defined. The blue curve above is your inverse function.