Answer
$6858,124,2743,63,511,124,1727,4095$,
$f^{-1}=\sqrt[3] {x+1}$
Work Step by Step
Step 1. Find the numeric values of each letter in "SEND HELP" as $19,5,14,4,8,5,12,16$
Step 2. Use the function $f(x)=x^3-1$ to calculate the numeric values for the above numbers as $6858,124,2743,63,511,124,1727,4095$ which are the encoded message.
Step 3. The inverse function of $f(x)$ can be found as $f^{-1}=\sqrt[3] {x+1}$
