Functions follow some basic rules. For the following examples, we'll use these functions:

- \( a(x) = x^2 \)
- \( b(x) = x+3 \)
\( c(x) = 4x \)

Addition: \( (f+g)(x) = f(x) + g(x) \), so for example, \( (b+c)(x) = 5x + 3 \).

- Multiplication: \( ( f\cdot g)(x) = f(x) \cdot g(x) \), so for example \( (a\cdot b)(x) = x^2 + 3x^2 \).

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