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? 

Observe that $f(x-\frac{1}{x})= x^3-\frac{1}{x^3}=(x-\frac{1}{x})^3+3\cdot x\cdot \frac{1}{x}\cdot(x-\frac{1}{x})=(x-\frac{1}{x})^3+3(x-\frac{1}{x})$
Hence, we can say that $$f(z)=z^3+3z$$ where $z$ is any real variable.
So we have that $$\color{red}{f(-x)}=\color{blue}{-x^3-3x}$$
