Checking Identity through Composite Functions

00:00 3 marks

Let \(f(x) = 3x + 2\) and its inverse be \(f^{-1}(x)\). Verify that composing \(f\) with its inverse gives the identity function, that is, show that \(f\left(f^{-1}(x)\right) = x\) for all \(x\).

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Hint

Recall that the inverse function reverses the effect of \(f\), so their composition should yield \(x\).

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The inverse function is \(f^{-1}(x) = \frac{x-2}{3}\), and the composition \(f(f^{-1}(x))\) simplifies to \(x\), verifying the identity function.

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Checking Identity through Composite Functions

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Checking Identity through Composite Functions

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