So you can express x_{3}and x_{4}in terms of x_{1}?

Then these constraints

in terms of x_{1}and x_{2}, and very soon in terms of f(x_{1}, x_{2}), which you've called f(x_{1}) but is apparently a function of two variables.

So that gives you two upper limits on f(x_{1}, x_{2}). The lower one then determines a relation between x_{1}and x_{2}.