SOLUTION: Given f(x)= x^3+x+4, find the f^-1(1) accurate to two decimal places

Left side is a monotonic function of x on the entire number line (over all real numbers),
because the derivative function 3x^2 + 1 is positive everywhere.


Therefore, the inverse function f^-1(x) does exist and is defined over all number line, too.


To find the value f^-1(x), it is enough to solve equation

    x^3 + x + 4 = 1,  or,  equivalently,  x^3 + x + 3 = 0.


I used online free of charge solver https://www.mathportal.org/calculators/solving-equations/polynomial-equation-solver.php


Below is the solution produced by the solver.


x1 = −1.21341
​
x2 = 0.60671 + 1.45061*i
​
x3 = 0.60671 − 1.45061*i
​
 
Explanation

This polynomial has no rational roots that can be found using Rational Root Test.

Roots were found using cubic formulas.


So, the unique real value/root/solution is  x = −1.21,  rounded to two decimal places.