Exploring the Identity Function in Composition

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Prove that for any function \(f\) defined on \(\mathbb{R}\), composing \(f\) with the identity function, defined by \(Id(x)=x\), yields \(f\). In other words, show that \((f \circ Id)(x)=f(x)\) for all \(x\in\mathbb{R}\).

Hint Hint

Hint

Recall the definition of the identity function, \(Id(x) = x\), and the definition of function composition, \((f \circ g)(x) = f(g(x))\).

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Complete Answer

For any function \(f\), we have \((f\circ Id)(x) = f(Id(x)) = f(x)\) for all \(x\in\mathbb{R}\).

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