Answer
This is a decomposition reaction.
Work Step by Step
In a decomposition reaction, one single reactant splits into two different products.
In this reaction, the $HI$ splits into $H_2$ and $I_2$, which is characteristic of decomposition reactions.
Pattern for decomposition reactions: $AB --\gt A + B$
That reaction: $HI(g) --\gt H_2(g) + I_2(g)$
