The domain of the function f(x)=4x+8(2/3) (x−2)−52−22(x−1)

Given that f(x)=4x+8(2/3) (x−2)−52−22(x−1) =4x+(23)(2/3) (x−2)−52−22(x−1) =4x+22(x−2)−52−22(x−1) f(x)=4x+4x−2−52−4(x−1) f(x)  is defined if 4x+4x−2−52−4(x−1)≥0 ⇒ 4x+4x16−52−4x4≥0  Let 4x=a ⇒a+a16−52−a4≥0 ⇒13a−832≥0 ⇒a−64≥0 ⇒a≥64 ⇒4x≥43         (∵   a=4x) ⇒x≥3 ⇒x∈[3,∞) ∴  Domain of  f(x)  is [3,∞)