A real valued function f satisfies f10-x - f10-x and f20-x - -f20-x- for all x - R which of the following statements is true-

The correct option is A f is an even function ∵ f(10+x)=f(10 x) f(20 x)= f(20+x) ∀ xϵ R if f( x) then f(10 x)=f(10 ( x)) f(10 x) ...

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Byju's Answer

Standard XII

Mathematics

Sum of n Terms

A real valued...

Question

A real valued function f satisfies f(10+x) = f(10-x) and f(20-x) = -f(20+x), for all $x \in R$ which of the following statements is true?

f is an even function

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f is an odd function

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f is a constant function

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f is a non-periodic function

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Solution

The correct option is A f is an even function
$∵ f (10 + x) = f (10 - x) f (20 - x) = - f (20 + x) \forall x ϵ R i f f (- x) t h e n f (10 - x) = f (10 - (- x)) f (10 - x) = f (10 + x) ∵ f (x) = f (- x) s o f i s a n e v e n f u n c t i o n .$

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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?

The correct option is A f is an even function∵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.

A real valued function f satisfies f(10+x) = f(10-x) and f(20-x) = -f(20+x), for all $x \in R$ which of the following statements is true?

The correct option is A f is an even function
$∵ f (10 + x) = f (10 - x) f (20 - x) = - f (20 + x) \forall x ϵ R i f f (- x) t h e n f (10 - x) = f (10 - (- x)) f (10 - x) = f (10 + x) ∵ f (x) = f (- x) s o f i s a n e v e n f u n c t i o n .$