<s>[INST] How to find this function, and what method to use? The function is $f(x-\frac{1}{x})= x^3-\frac{1}{x^3}$ and they are asking us to find out what $f(-x)$ is? 
 [/INST] As per Parth Kohli's comment we can write $$f\left(x - \frac{1}{x}\right) = \left(x - \frac{1}{x}\right)^3 + 3\left(x - \frac{1}{x}\right).$$
That is, $f(x) = x^3 + 3x$ so $f(-x) = (-x)^3 + 3(-x) = -(x^3 + 3x)$. 
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