If $f (x) = 3 x^{4} - 9 x + 1$ , then $f (x + 1) =$

3 x^{4} + 12 x^{3} + 18 x^{2} + 3 x - 5

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3 x^{4} - 12 x^{3} - 18 x^{2} + 3 x - 5

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3 x^{4} - 18 x^{2} + 3 x

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3 x^{4} + 18 x^{2} - 3 x

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Solution

The correct option is A $3 x^{4} + 12 x^{3} + 18 x^{2} + 3 x - 5$
Given, $f (x) = 3 x^{4} - 9 x + 1$
Replace $x \to x + 1$ , we get
$f (x + 1) = 3 {(x + 1)}^{4} - 9 (x + 1) + 1$
$= 3 (x + 1)^{2} (x + 1)^{2} - 9 x - 9 + 1$
$= 3 x^{4} + 12 x^{3} + 18 x^{2} + 3 x - 5$

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