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

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$x^{4} + 1$

$x^{4} - 2 x^{2} + 2$

$x^{4} - 6 x^{3} + 2 x^{2} + 21 x + 12$

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

answer is C.

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Detailed Solution

$f (x^{2} - 3 x - 2) = {(x^{2} - 3 x - 2)}^{2} - 3 (x^{2} - 3 x - 2) + 2 = x^{4} + 9 x^{2} + 4 - 4 x^{2} + 12 x - 6 x^{3} - 3 x^{2} + 9 x + 6 + 2 = x^{4} - 6 x^{3} + 2 x^{2} + 21 x + 12$

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