The domain of definition of function fx=sin-12x+π6for real values of x, is

Given,fx=sin-12x+π6To find domain, we must havesin-12x+π6≥0             but -π2≤sin-1θ≤π2Now,         -π6≤sin-12x≤π2⇒sin-π6≤2x≤sinπ2⇒-12≤2x≤1⇒-14≤x≤12x∈-14,12