A question about Convex feasibility problem

Hypothetically,there is a set of convex constraints:

I just want to know if there is a x meeting all the constraints.
can i use cvx to find x?

Yes, if the constraints can be written following CVX’s DCP rules. If you just want to find out if there is an x satisfying all the constraints, just include all the constraints in your CVX program, and do not include a minimize or maximize statement.

You can read the CVX Users’ Guide .

You can also read Why isn't CVX accepting my model? READ THIS FIRST!

Thanks a lot.
And the “Status: Infeasible Optimal value (cvx_optval): +Inf” says that there is not any x satisfying all the constraints,right?
If so,what’s the situation when “Status: failed”?

I think "Status: failed” means the solver failed, usually due to numerical difficulties. If a problem produced such a message, can you show us a complete reproducible problem, preferably with all input data, as well as all the solver and CVX output?

If the solver fails due to numerical difficulties, it is often because of bad numerical scaling in the input data. All non-zero input data should be within s small number of orders of magnitude of one. If Mosek is used as solver, it provides warning messages if any of the non-zero input data is very large or very small in magnitude.