Hello

The problem states:

IF $\displaystyle f(\frac{1}{x})=x^2+\frac{1}{x^3}$ AND $\displaystyle g(x)= \frac{1}{2}(f(x)+f(-x))$ THEN $\displaystyle g(x)=?$

So, I got that $\displaystyle f(x)=\frac{1}{x^2}+\frac{x^3}{1}$ and that $\displaystyle f(-x)=\frac{1}{x^2}-\frac{x^3}{1}$

That gives me $\displaystyle g(x)=\frac{1}{2}*\frac{2}{x^2}=\frac{1}{x^2}$

Is this correct? I had huge problems with this as I was always getting $\displaystyle g(x)=\frac{1}{2}*0$... then I figured my mistake: $\displaystyle f(-x)$ is not equal to $\displaystyle (-f(x))$