Composition of functions involves chaining functions together so that the output of one function becomes the input of another. It is denoted \( (f \circ g)(x) = f(g(x)) \).
- \( a(x) = x^2, \)
- \( b(x) = x+3, \)
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 \( (a \circ b)(x) \).