  We present new results concerning threshold functions for a wide family of
random intersection graphs. To this end we apply the coupling method used for
establishing threshold functions for homogeneous random intersection graphs
introduced by Karo\'nski, Scheinerman, and Singer--Cohen. In the case of
inhomogeneous random intersection graphs the method has to be considerably
modified and extended. By means of the altered method we are able to establish
threshold functions for a general random intersection graph for such properties
as $k$-connectivity, matching containment or hamiltonicity. Moreover using the
new approach we manage to sharpen the best known results concerning homogeneous
random intersection graph.
