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Question

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


A
(x73)12
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B
(x+73)12
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C
(x37)12
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D
(x+37)12
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Solution

The correct option is A $$\left(\dfrac{x - 7}{3}\right)^{\dfrac{1}{2}}$$
If $$f(x)=3x+10 \quad g(x)=x^2+1$$ then $$(fog)^{-1}$$
$$f(g(x))=3(g(x))+10$$
$$=3(x^2-1)+10$$
$$\Rightarrow 3x^2-3+10$$
$$fog \Rightarrow 3x^2+7$$
$$(fog)^{-1}\Rightarrow \sqrt{\cfrac{y-7}{3}}=x$$

Mathematics

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