Find $g (x)$ , if $f (x) = 7 x + 12$ and $f (g (x) = 21 x^{2} + 40$

21 x^{2} + 28

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21 x^{2}

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7 x^{2} + 4

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3 x^{2} + 28

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3 x^{2} + 4

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Solution

The correct option is E $3 x^{2} + 4$
Given, $f (x) = 7 x + 12, f (g (x)) = 21 x^{2} + 40$
$∴ f (g (x)) = 7 g (x) + 12 = 21 x^{2} + 40$
$∴ 7 g (x) = 21 x^{2} + 28$
$∴ g (x) = 3 x^{2} + 4$

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