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Composite Function

If fx=2x+1 ...

Question

If $f (x) = 2 x + 1$ and $g (x) = x^{2} + 1$ then $(g o (f o f)) (2) =$

112

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122

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12

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124

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Solution

The correct option is A $122$
$(g o (f o f)) (x) = g (f (f (x)))$
$= g (f (2 x + 1))$
$= g (2 (2 x + 1) + 1)$
$= g (4 x + 3)$
$= {(4 x + 3)}^{2} + 1$
$(g o (f o f)) (2) = {(11)}^{2} + 1 = 122$

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