GATE (Graduate Aptitude Test in Engineering) Computer Science & IT (CS) Mathematical Logic-Propositional Logic Study Material (Page 16 of 17)

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Function Composition

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Function Composition

  • This is a very simple topic and things get better also because it features regularly in exam. Thus, it is expected that Students treat this topic as “Marks guaranteed” . The theory is not expected, we only need the ability to substitute functions.
  • In mathematics, function composition is the concept of pointwise application of one function to the result of another in order to produce a third function. For instance, the functions f: X ⇾ Y and g: Y ⇾ Z can be composed to yield a function which maps x in X …

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Function Composition: Properties

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Properties

The composition of functions is always considered to be an associative property. It is a property inherited from the composition of relations. That is, if f, g, and h are three functions which have suitably chosen domains and codomains, then we can say that f ∘ (g ∘ h) = (f ∘ g) ∘ h, where the parentheses serve to indicate that composition is to be performed first for the pa…

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