6is the ans 2?
let f1(x) = x for 0≤x≤1
1 for x>1
0 otherwise
and
f2(x) = f1(-x) for all x
f3(x) = -f2(x) for all x
f4(x) = f3(-x) for all x
Which of the following in necessarily true?
1. f4(x) = f1(x) for all x
2. f1(x) = - f3(-x) for all x
3. f2(-x) = f4(x) for all x
4. f1(x) + (3(x) = 0 for all x
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4 Answers
1f1(x) = x for 0≤x≤1
1 for x>1
0 otherwise
f2(x) =f1(-x)
f2(x) = -x for 0≥x≥-1
1 if x<-1
0 if x>0
f3(x) = -f2(x)
f3(x) = x for 0≥x≥-1
-1 if x<-1
0 if x>0
f4(x) = f3(-x)
f4(x) = -x for 0≤x≤1
-1 for x>1
0 for x<0
So f1(x) = -f4(x) = -f3(-x) for all x in the domain.