In Sakurai, it is stated that,
the coefficients (Clebsch-Gordan Coefficients) vanish unless $|j_1 − j_2| \le j \le j_1 + j_2$.
In the book it is just given that the relation is satified. But I am asking for a formal proof regarding this.
Ref - Modern Quantum Mechanics-2nd ed (Sakurai) (eqn no. - 8.38)
