If the events A and B arc mutually exclusive events such that P(A)=3x+13 and P(B)=1−x4, then the set of possible real values of x lies in the interval

We must have,0≤P(A)≤1⇒0≤3x+13≤1⇒−13≤x≤23            (1)and 0≤P(B)≤1⇒ 0≤1−x4≤1⇒ −3≤x≤1           (2)and 0≤P(A∪B)=P(A)+P(B)≤1⇒ 0≤3x+13+1−x4≤1⇒ −79≤x≤59          (3)From (1), (2) and (3), we get x∈−13,59.