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

x^{2} - 1

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x^{4} - 2 x^{2}

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x^{8} + 4 x^{4} - 4 x^{6}

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x^{8} + 4 x^{4} - 4 x^{6} - 1

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Solution

The correct option is D $x^{8} + 4 x^{4} - 4 x^{6} - 1$
$Given f (x) = x^{2} - 1$
$f o f o f = f {f [f (x)]}$
$= f {f [x^{2} - 1]} = f {(x^{2} - 1)^{2} - 1} = f {x^{4} + 1 - 2 x^{2} - 1} = f {x^{4} - 2 x^{2}} = (x^{4} - 2 x^{2})^{2} - 1 = x^{8} + 4 x^{4} - 4 x^{6} - 1$

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