So I'm just about done with my latest assignment, however there's this little vermin impeding my way towards a perfect score. I think I may have nailed the answer, but given that it's my last available attempt at submitting a response, I want to beextrasure.

Some background information before the actual question:

The function...

The expression $\displaystyle f(x)$ is defined exactly on the set...

The expression $\displaystyle f(x)$ is equal to zero if $\displaystyle x$ is equal to...

The set of all real numbers $\displaystyle x$ for which $\displaystyle f(x)$ is defined and non-zero is...

And so, here is what's currently holding me back...

By analyzing the sign of $\displaystyle f(x)$ on the above open intervals, solve the inequality...

... expressing answer in interval notation.

My answer to this was:

Is it correct?