Is it always true that the inverse function should yield a straight line? Some of the practice problems that I have done did not seem to create a linear line via the inverse function. So I wanted to know if the inverse of any equation should give a straight line or is it only certain types of equations.

I can't tell from your question exactly what situations you are referring to. Hopefully the statement I give you below will answer your question; if not, please ask again with more specifics.
For many things that we observe in the real world, either the log(y) vs. log(x) graph, the log(y) vs. x graph or the y vs. log(x) graph will be a straight line.
When this is the case we can then obtain the equation of the appropriate function.
However this is not always the case.