# Composition of Functions

Composition of functions involves chaining functions together so that the output of one function becomes the input of another. It is denoted $$(f \circ g)(x) = f(g(x))$$.

Given

• $$a(x) = x^2,$$
• $$b(x) = x+3,$$

we can evaluate $$(a \circ b)(x) = a(x+3) = (x+3)^2$$.

While addition and multiplication of functions is commutative (i.e., $$f+g = g+f$$), the composition of functions is not. Note that $$(b \circ a)(x) = b(x^2) = x^2+3$$ is not the same as $$(a \circ b)(x)$$.

Note by Arron Kau
3 years, 10 months ago

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