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Class-11-science»Maths

If f(x)=x3+1/x3 then find the value of f(x)-1/f(x)

Given f (x) = x^{3} + \frac{1}{x^{3}} Consider f (x) - f (\frac{1}{x}) = x^{3} + \frac{1}{x^{3}} - [{(\frac{1}{x})}^{3} + \frac{1}{{(\frac{1}{x})}^{3}}] = x^{3} + \frac{1}{x^{3}} - \frac{1}{x^{3}} - \frac{1}{\frac{1}{x^{3}}} = x^{3} - x^{3} = 0 So, f (x) - f (\frac{1}{x}) = 0

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