Problem

1. Assume a (real valued) function $y=f(x)$ satisfy $y^5+9y=x^3+x$. Suppose $g(x)$ is a (real valued) function satisfying $f(g(x))=x$.

(a) $(5\%)$ The value $g(1)$ must be $2$. True or false? Answer: $\underline{\quad(1)\quad}$.

(b) $(10\%)$ The derivative $g'(1)=\underline{\quad(2)\quad}$.