If $f (x) = 4 x^{2} - 1$ and $g (x) = 8 x + 7, g^{o} f (2) =$

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127

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345

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2115

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Solution

The correct option is C 127
Since $g o f (x) = g (f (x))$
It is given that $f (x) = 4 x^{2} - 1$ and $g (x) = 8 x + 7$
Therefore, $g o f (x) = g (f (x))$
$= g (4 x^{2} - 1)$
$= 8 (4 x^{2} - 1) + 7$
$= 32 x^{2} - 8 + 7$
$= 32 x^{2} - 1$
Thus, $g o f (x) = 32 x^{2} - 1$
Now substitute $X = 2$ in $g o f (x) = 32 x^{2} - 1$ as shown below:
$g o f (2) = 32 (2)^{2} - 1 = 128 - 1 = 127$

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