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: g of x equals the cube root of x minus 3. 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 h(x) = { f(x) if  x<0           (see photo)                                                                                                         { h(x) if x≥0                                                                               Are there any breaks in the domain of h (x)? Explain why or why not. Show all necessary calculations.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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: g of x equals the cube root of x minus 3.

Part A: Using the Factor Theorem, determine the polynomial function f (x) in expanded form. Show all necessary calculations.

Part B: Let (x) be the piecewise defined function of h(x) = { f(x) if  x<0           (see photo)

                                                                                                        { h(x) if x≥0                                                                               Are there any breaks in the domain of (x)? Explain why or why not. Show all necessary calculations.

h(x) =
[f(x)
(g(x)
if x<0
if x>0°
Transcribed Image Text:h(x) = [f(x) (g(x) if x<0 if x>0°
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