In general, the composition of functions is not ___.
commutative
In general, the composition of functions is not commutative.
Commutative property means that changing the order of operands doesn’t change the result. However, this is not true for the composition of functions, i.e., for two functions f and g, (f∘g) is not necessarily equal to (g∘f).
For example, let f(x) = 2x and g(x) = x + 3, then (f∘g)(x) = f(g(x)) = f(x+3) = 2(x+3) = 2x + 6, and (g∘f)(x) = g(f(x)) = g(2x) = 2x + 3. Clearly, (f∘g)(x) ≠ (g∘f)(x).
However, sometimes the composition of functions can be commutative, such as when f and g are inverse functions, i.e., f(g(x)) = g(f(x)) = x. In general, unless f and g are specifically defined to be commutative, the composition of functions is not commutative.
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