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`g(f(x))={([f(x)]",",-pi le f(x) lt 0),(sin f(x)",",0 le f(x) le pi):}` <br> `={([[x]]",",-pi le [x] lt 0",",-2 le x le -1),([|x|+1]",",-pi le |x| +1 lt 0",",-1 lt x le 2),(sin[x]",",0 le [x] le pi",",-2 le x le -1),(sin(|x|+1)",",0le |x|+1 le pi",",-1 lt x le 2):}` <br> `={([x]",",-2 le x le -1),(sin(|x|+1)",", -1 lt x le 2):}` <br> Hence, the domain is [-2, 2]. <br> Also, for `-2 le x le -1, [x]= -2, -1,` <br> and for `-1 lt x le 2, |x| +1 in [1,3]` <br> ` :. sin (|x|+1) in [sin 3,1]` <br> Hence, the range is `{-2, -1} cup [sin 3,1].` <br> Also, for `y in [sin 3,1], [y]=0,1.` <br> Hence, the number of integral points in the range is 4.