The domain of cos−1x−54−log10(6−x)  is

Let f(x)=  cos−1x−54−log10(6−x) cos−1(x−54)  is defined if −1≤x−54≤1⇒−4≤x−5≤4⇒1≤x≤9⇒x∈[1,9].........(1)log(6−x)  is defined if 6−x>0 ⇒x<6⇒x∈(−∞,6)......(2)From (1)&(2)  ( take the intersection of the two domains )  , we get x∈[1,6)    ∴  Domain of f(x)  is [1,6)