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find the composition of function for the given function.

find the composition of function for the given function.

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Grade:11

2 Answers

Aashrut
27 Points
4 years ago
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+x
If x belongs to (1,2] and f(x) belongs to (2,3] then 
f{f(x)} = f{1+x}= 3-(1+x)= 2-x
If x belongs to (2,3] and f(x) belongs to [0,1) then 
f{f(x)} = f{3-x} = 1+(3-x)= 4-x
So finally, the answer is
f{f(x)} = 2 + x,  if 0 ≤ x ≤ 1
              2 - x, if 1
              4 -x   if 2
 
Aashrut
27 Points
4 years ago
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

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