Question

$f(x)=\frac{3-x}{x}$
encontrar$f(x^{2} )-(f(x))^{2}$

Answer 1

$f(x) = \frac{ 3 - x}{x}$

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$f( {x}^{2}) = \frac{3 - {x}^{2} }{ {x}^{2} }$

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$(f(x) ){}^{2} = \frac{ {(3 - x)}^{2} }{ {x}^{2} } \\ {(f(x))}^{2} = \frac{ {x - 6x + 9}^{2} }{ {x}^{2} }$

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$= f( {x}^{2} ) - (f(x)) {}^{2} \\ = \frac{3 - {x}^{2} }{ {x}^{2} } - \frac{ {x}^{2} - 6x + 9}{ {x}^{2} } \\ = \frac{ - {x}^{2} - {x}^{2} + 6x + 3 - 9}{ {x}^{2} } \\ = \frac{ - 2 {x}^{2} + 6x - 6 }{ {x}^{2} }$