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$f (x) = 3 x + 5$ , $g (x) = f^{- 1} (x)$ then $g (3) = ?$

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- \frac{2}{3}

\frac{2}{3}

answer is C.

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Detailed Solution

f (x) = 3 x + 5

Let $f (x) = y \Rightarrow x = f^{- 1} (y)$

$3 x + 5 = y$ $3 x = y - 5 \Rightarrow x = \frac{y - 5}{3}$

$\Rightarrow f^{- 1} (y) = \frac{y - 5}{3}$

$∴ f^{- 1} (x) = \frac{x - 5}{3}$

$g (3) = f^{- 1} (3) = \frac{3 - 5}{3} = \frac{- 2}{3}$

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