How to use conditional (piecewise) function in cvx?

Let us consider the function f(x), defined as f(x)=x for negative x+10, f(0)=10, and f(x)=ln(1+x)+10 for positive x. It is clear that f(x) is a concave and smooth function.

I coded it as

if x<0
maximize f
subject to blah blah blah

However, since x is posed in “if” statement, error occurs. Is there any method to implement CVX for the case where the objective function is differently defined according to design variable’s region.

Have you followed the advice to read the link provided in answer to your previous question? How can I maximize a piecewise concave function?

I already read the MOSEK link which is given in an answer for my previous question. However, since there are no code examples, I cannot implement my program.

The document proposed a method to convert a piecewise function into another form by introducing dummy variable t (based on the epigraph notion).

However, I do not grasp what should be maximized.