$If f (x) = x^{2} + 1, then find f o f$ .

x^{2} + 1

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x^{4} + 2 x^{2} + 1

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x^{4} + 2 x^{2} + 2

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x^{2} + 2 x^{2} + 2

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Solution

The correct option is C $x^{4} + 2 x^{2} + 2$
$Given, f (x) = x^{2} + 1$
$∵ f o f (x) = f (f (x))$
$= f (x^{2} + 1) = (x^{2} + 1)^{2} + 1 = ((x^{2})^{2} + 1 + 2 x^{2}) + 1 = x^{4} + 2 x^{2} + 2$

$∴ f o f (x) = x^{4} + 2 x^{2} + 2$

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