Let f(x) be a polynomial function with a zero of multiplicity of 1 at 3 and a zero of multiplicity of 2 at 1. Let g(x) be the radical function [tex]g(x)=\sqrt[3]{x} -3[/tex]
Part A: Using the Factor Theorem, determine the polynomial function f (x) in expanded form. Show all necessary calculations.
Part B: Let h(x) be the piecewise defined function of [tex]h(x)=\left \{ {{f(x) (x\ \textless \ 0)} \atop {g(x) (x\geq 0)}} \right.[/tex] Are there any breaks in the domain of h(x)? Explain why or why not. Show all necessary calculations.