Find the correct expression for $f (g (x))$ given that $f (x) = 4 x + 1$ and $g (x) = x^{2} - 2$

- x^{2} + 4 x + 1

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x^{2} + 4 x - 1

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4 x^{2} - 7

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4 x^{2} - 1

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16 x^{2} + 8 x - 1

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Solution

The correct option is C $4 x^{2} - 7$
Given, $g (x) = x^{2} - 2$
$f (g (x)) = f (x^{2} - 2)$
Also given, $f (x) = 4 x + 1$
$∴ f (x^{2} - 2) = 4 (x^{2} - 2) + 1$
$\Rightarrow 4 x^{2} - 8 + 1$
$\Rightarrow 4 x^{2} - 7$

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