find the composition of function for the given function.

If x belongs to [0 ,2] then f(x) belopngs to [1, 3].If x belongs to (2,3] then f(x) belongs to [0,1).So for f{f(x)} the new input will be [1,3] and [0,1).So if x belongs to [0,1] and f(x) belongs to [1,2] then f{f(x)}= f{1+x}=1+(1+x)= 2+xIf x belongs to (1,2] and f(x) belongs to (2,3] then f{f(x)} = f{1+x}= 3-(1+x)= 2-xIf x belongs to (2,3] and f(x) belongs to [0,1) then f{f(x)} = f{3-x} = 1+(3-x)= 4-xSo finally, the answer isf{f(x)} = 2 + x, if 0 ≤ x ≤ 1 2 - x, if 1 4 -x if 2