Trigonometric equations

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Question

If $f$ is periodic, $g$ is non- periodic and $f (g (x))$ is periodic and $g (2) = 3, g (4) = 7$ , then $g (6) =$

Moderate

Solution

$g (x)$ must be a linear function
$\Rightarrow g (x) = a x + b$
$Sin c e g (2) = 3, g (4) = 7$
$\Rightarrow g (x) = 2 x - 1$
$∴ g (6) = 11$

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