Hey guys, so i have this problem from my final exam, and I have no clue on how to do and would like to actually understand it (I uploaded the pic of the problem below).

It is about finding the value of a that makes h(x)g(x). I know that a function is continuous at a point if the limit exists on both sides and that the limit is at the same value. However, I never dealt with product of functions and how to find if there's a value for a that makes the product of functions continuous.

How would i otherwise prove or disprove that there's a value for a?

[PIC] https://imgur.com/a/QDnGe