In a combination reaction, two elements or compounds combine to form, a new compound, whereas in decomposition reactions, a compound decomposes to give two or more elements or compounds.
Thus, combination and decomposition reactions are opposite of each other :
Combination reaction :
2Mg(s) + O2(g) → 2MgO(s)
Decomposition reaction:
CaCO3(s) → CaO(s) + CO2(g).