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Standard XII
Maths
Question

A real valued function f satisfies f(10+x) = f(10-x) and f(20-x) = -f(20+x), for all x∈R which of the following statements is true?
  1. f is an even function
  2. f is an odd function
  3. f is a constant function
  4. f is a non-periodic function

A
f is a constant function
B
f is an odd function
C
f is an even function
D
f is a non-periodic function
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Solution
Verified by Toppr

∵f(10+x)=f(10−x)f(20−x)=−f(20+x)∀xϵRiff(−x)thenf(10−x)=f(10−(−x))f(10−x)=f(10+x)∵f(x)=f(−x)sofisanevenfunction.

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