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UPSC NDA I 2024 Mathematics Paper

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Consider the following for the next two (02) items that follow :

Let

f(x)

and

g(x)

be two functions such that

g(x)=x-\;\frac{1}{x}

and

f \circ g(x)=x^3-\;\frac{1}{x^3}

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Question : 85 of 120

Marks: +1, -0

What is

g[f(x)-3x]

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

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