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Q.

Let f1(x)=x,0≤x≤11, x>10, otherwise f2(x)=f1(−x) for all xf3(x)=−f2(x) for all xf4(x)=f3(−x) for all xwhich of the following is necessarily true?

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a

f4(x)=f1(x) for all x

b

f1(x)=−f3(−x) for all x

c

f2(−x)=f4(x) for all x

d

f1(x)+f3(x)=0 for all x

answer is B.

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Detailed Solution

f2(x)=f1(-x) f3(x)=-f2(x) f3(x)=-f1(-x) replace x by -x f3(-x)=-f1(x) ⇒f1(x)=-f3(-x)
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