Mathematics

Problem

Let

g

be the function defined by

g(x)=\begin{cases} x^{3}-3x, & -2\le x\le 1,\\ 4-x, & 1<x\le 4. \end{cases}

Does the equation

g(x)=1

have at least one real solution in the interval

(1,4]

? Answer Yes or No and name a specific closed interval of length

1

contained in

(1,4]

on which such a solution is guaranteed to lie.