Math Problem Statement
If two functions f(x) and g(x) are commutative with period p, show that the function af(x) + bg(x) with any fixed number a, b is also periodic with period p
Solution
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Math Problem Analysis
Mathematical Concepts
Periodicity
Commutativity
Linear Combination of Functions
Formulas
f(x + p) = f(x)
g(x + p) = g(x)
h(x) = a f(x) + b g(x)
h(x + p) = h(x)
Theorems
Periodicity Theorem
Commutativity
Suitable Grade Level
Undergraduate Level