Question

Fx = x+1/x prove that (fx)³=f(x³)+3f(1/x)

Answer 1

Hope u like my process
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$= > \bf \: f(x) = x + \frac{1}{x} \\ \\ = > \bf f( {x}^{3}) = {x}^{3} + \frac{1}{ {x}^{3} } \\ \\ = > \bf \: f( \frac{1}{x} ) = \frac{1}{x} + x = x. \frac{1}{x}(x + \frac{1}{x} ) \\ \\ = > \bf \: (f(x)) ^{3} = {(x + \frac{1}{x}) }^{3} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \bf {x}^{3} + \frac{1}{ {x}^{3} } + 3x. \frac{1}{x} (x + \frac{1}{x} ) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \bf \: f( {x}^{3} ) + 3f( \frac{1}{x} )$
Hence, proved.

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