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If f(x)=x+1/x show that (f(x))^3=f(x^3)+...

If `f(x)=x+1/x` show that `(f(x))^3=f(x^3)+3 f(x)`

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We have `f(x)=x+1 / x`
`(f(x))^3=(x+1 / x)^3=x^3+1 / x^3+3 x cdot 1 / x(x+1 / x) .=(x^3+1 / x^3)+3(x+1 / x)=f(x^3)+3 f(x)`
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