Let f and g be two bijective functions defined on a set A, such that $f (x) = 2 x + 1 and (g \circ f) (x) = 3 x + 2 . Then g (x)$ is.

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$2 x - \frac{3}{2}$

$\frac{3}{2} x - \frac{5}{2}$

$\frac{3}{2} x + \frac{1}{2}$

$5 x + 3$

answer is B.

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Detailed Solution

$\begin{array}{l} f (x) = 2 x + 1 \\ y = 2 x + 1 \Rightarrow x = \frac{y - 1}{2} \end{array}$

$\begin{array}{l} ∴ f^{- 1} (x) = \frac{x - 1}{2} \\ ∴ g (x) = (g \circ f) f^{- 1} (x) \\ = (g \circ f) (\frac{(x - 1)}{2}) \\ = \frac{3 (x - 1)}{2} + 2 = \frac{1}{2} (3 x + 1) \end{array}$

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