If $g (x) = 2 x + 1$ and $h (x) = 4 x^{2} + 4 x + 7$ , find a function $f$ such that $f o g = h$

f (x) = x^{3} - 6

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f (x) = x^{2} + 6

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f (x) = x^{2} - 6

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f (x) = (2 x + 1)^{2} + 6

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Solution

The correct option is C $f (x) = x^{2} + 6$
$f (g (x)) = h = 4 x^{2} + 4 x + 7 = (2 x + 1)^{2} + 6 = (g (x))^{2} + 6$

$\Rightarrow f (x) = x^{2} + 6$

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