The domain of the function f(x)=cos−1⁡2−|x|4+[log⁡(3−x)]−1 is

cos−1⁡2−|x|4 is defined for −1≤2−|x|4≤1 ⇒−4≤2−|x|≤4⇒−6≤−|x|≤2⇒−2≤|x|≤6⇒|x|≤6⇒−6≤x≤6   ....(1)1log⁡(3−x) is defined if log (3 – x) ≠ 0 and 3 – x > 0⇒3−x≠e0=1 and x<3⇒x≠2 and x<3From Eq. (1) and (2), we get domain of f= [– 6, 6] ∩ ((– ∞, 3) \ {2}) = [– 6, 3)\{2}.