If $f (x) = 3 x + 10, g (x) = x^{2} - 1$ , then $(f o g)^{- 1}$ is equal to

{(\frac{x - 7}{3})}^{\frac{1}{2}}

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{(\frac{x + 7}{3})}^{\frac{1}{2}}

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{(\frac{x - 3}{7})}^{\frac{1}{2}}

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{(\frac{x + 3}{7})}^{\frac{1}{2}}

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Solution

The correct option is A ${(\frac{x - 7}{3})}^{\frac{1}{2}}$
If $f (x) = 3 x + 10 g (x) = x^{2} + 1$ then $(f o g)^{- 1}$
$f (g (x)) = 3 (g (x)) + 10$
$= 3 (x^{2} - 1) + 10$
$\Rightarrow 3 x^{2} - 3 + 10$
$f o g \Rightarrow 3 x^{2} + 7$
$(f o g)^{- 1} \Rightarrow \sqrt{\frac{y - 7}{3}} = x$

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