Set, Relation and FunctionHard
Question
Let f: R → R be a function such that f(2 − x) = f(2 + x) and f(4 − x) = f(4 + x), for all x ∈ R and 
dx = 5. Then the value of 
dx is :
dx = 5. Then the value of dx is :Options
A.125
B.80
C.100
D.200
Solution
Put x = 2 + x
f(-x) = f(4 + x) = f(4 - x)
⇒ f(x) = f(x + 4)
Hence period is 4
= 10[5 + 5]
= 100
f(-x) = f(4 + x) = f(4 - x)
⇒ f(x) = f(x + 4)
Hence period is 4
= 10[5 + 5]
= 100
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