Given $f (x) = 4 x + 2$ . Find $a$ , if $f (a + 1) = f (2)$

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Solution

Given, $f (x) = 4 x + 2$
Therefore, $f (a + 1) = 4 (a + 1) + 2 = 4 a + 4 + 2 = 4 a + 6$
and $f (2) = 4 (2) + 2 = 8 + 2 = 10$
Also given, $f (a + 1) = f (2)$
$\Rightarrow 4 a + 6 = 10$
$\Rightarrow 4 a = 4$
$\Rightarrow a = 1$

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