Given, f(x)=sin‌−1(x2−1)−3log3(3x−2) −1≤x2−1≤1 0≤x2≤2 −√2<x<√2 ∴sin‌−1(x2−1) is not defined for (−∞,−√2) and (√2,0) For 3log3(3x−2)‌‌⇒‌‌3x−2>0 ‌3x>2 ‌x>log32 ∴3log3(3x−2) is not defined for x≤log3(2) So, intervel [−√2,√2] combine with x>log3(2). The domain of f(x) is $log_3(2) So, f(x) is not defined for ‌(−∞,log32)∪(√2,0) ‌a=log32,b=√2 ‌3a+b2=2+2=4