MHB Identity Function: Definition, Examples & Properties

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The identity function is defined as a function that maps every element of a set to itself, denoted as $id_A: A \to A$. It is characterized as a bijection, meaning it is both injective and surjective. The composition of the identity function with any other function $f$ results in the original function, expressed as $f \circ id_A = f$. The discussion highlights that the identity function maintains the properties of bijections when composed with other functions. Understanding the identity function is crucial for grasping more complex function properties in mathematics.
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dana said:
hey,
question is attached

thanks in advance!

Hi dana!

Well... since $id_A: A\to A$ is a bijection, it seems fair to me that $f \circ g: A \to A$ given by $f \circ g: a \mapsto a$ is also a bijection...
 

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