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Maths-

General

Easy

Question

If $f left parenthesis x right parenthesis$ and $straight g left parenthesis straight x right parenthesis$ are two functions with $g left parenthesis x right parenthesis equals x minus 1 over x text and fog end text left parenthesis x right parenthesis equals x cubed minus 1 over x cubed text , then end text f to the power of straight prime left parenthesis x right parenthesis text is end text$

$3 x^{2} + 3$
$x^{2} - \frac{1}{x^{2}}$
$1 + \frac{1}{x^{2}}$
$3 x^{2} + \frac{3}{x^{4}}$

The correct answer is: $3 x squared plus 3$

Since,
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell f open parentheses x minus 1 over x close parentheses equals x cubed minus 1 over x cubed end cell row cell f open parentheses x minus 1 over x close parentheses equals open parentheses x minus 1 over x close parentheses open parentheses x squared plus 1 over x squared plus 1 close parentheses end cell row cell equals open parentheses x minus 1 over x close parentheses open square brackets open parentheses x minus 1 over x close parentheses squared plus 3 close square brackets end cell row cell not stretchy rightwards double arrow f left parenthesis x right parenthesis equals x open parentheses x squared plus 3 close parentheses equals x cubed plus 3 x end cell row cell not stretchy rightwards double arrow f to the power of straight prime left parenthesis x right parenthesis equals 3 x squared plus 3 end cell end table$

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