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Properties of Inverse Function

If f: R → R i...

Question

If $f : R \to R$ is defined by $f (x) = x^{2} - 3 x + 2$ , write $f {f (x)}$ .

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Solution

Given that, $f (x) = x^{2} - 3 x + 2$

$∴ f {f (x)} = f (x^{2} - 3 x + 2) = (x^{2} - 3 x + 2)^{2} - 3 (x^{2} - 3 x + 2) + 2 = x^{4} + 9 x^{2} + 4 - 6 x^{3} - 12 x + 4 x^{2} - 3 x^{2} + 9 x - 6 + 2 = x^{4} + 10 x^{2} - 6 x^{3} - 3 x f {f (x)} = x^{4} - 6 x^{3} + 10 x^{2} - 3 x$

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