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$I f f : R \to R a n d g : R \to R a r e d e f i n e d b y f (x) = 2 x + 3 a n d g (x) = x^{2} + 7, t h e n v a l u e s o f x s u c h t h a t g (f (x)) = 8 a r e$

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An Intiative by Sri Chaitanya

a

$1, 2$

b

$1, - 2$

c

$- 1, - 2$

d

$- 1, 2$

answer is C.

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Detailed Solution

$\begin{array}{l} f (x) = 2 x + 3, g (x) = x^{2} + 7 \\ G i v e n g (f (x)) = 8 \\ \Rightarrow g (2 x + 3) = 8 \\ \Rightarrow {(2 x + 3)}^{2} + 7 = 8 \\ \Rightarrow {(2 x + 3)}^{2} = 1 \\ \Rightarrow 2 x + 3 = \pm 1 \\ \Rightarrow 2 x + 3 = 1, 2 x + 3 = - 1 \\ \Rightarrow x = - 1, x = - 2 \end{array}$

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