If the function f- 7- R satisfies the relation f x - f x - 4 -f x - 2 - f x - 6 br all x - R then a period of f is-

f(x)+f(x+4)=f(x+2)+f(x+6)→ (1) ⇒ f(x 2)+f(x+2)=f(x)+f(x+4) ⇒ f(x 2)+f(x)+f(x+4) f(x+6)=f(x)+f(x+4) ⇒ f(x 2)=f(x+6) f(x)=f(x+8) Period is ...

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Standard XII

Mathematics

Definition of Sets

If the functi...

Question

If the function $f : 7 \to R$ satisfies the relation $f (x) + f (x + 4) = f (x + 2) + f (x + 6) br all x \in R$ then a period of $f$ is:

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Solution

$f (x) + f (x + 4) = f (x + 2) + f (x + 6) \to (1) \Rightarrow f (x - 2) + f (x + 2) = f (x) + f (x + 4) \Rightarrow f (x - 2) + f (x) + f (x + 4) - f (x + 6) = f (x) + f (x + 4) \Rightarrow f (x - 2) = f (x + 6) f (x) = f (x + 8)$
Period is $8$

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If the function f:7→R satisfies the relation f(x)+f(x+4)=f(x+2)+f(x+6) br all x∈R then a period of f is:

f(x)+f(x+4)=f(x+2)+f(x+6)→(1)⇒f(x−2)+f(x+2)=f(x)+f(x+4)⇒f(x−2)+f(x)+f(x+4)−f(x+6)=f(x)+f(x+4)⇒f(x−2)=f(x+6)f(x)=f(x+8)Period is 8

If the function $f : 7 \to R$ satisfies the relation $f (x) + f (x + 4) = f (x + 2) + f (x + 6) br all x \in R$ then a period of $f$ is:

$f (x) + f (x + 4) = f (x + 2) + f (x + 6) \to (1) \Rightarrow f (x - 2) + f (x + 2) = f (x) + f (x + 4) \Rightarrow f (x - 2) + f (x) + f (x + 4) - f (x + 6) = f (x) + f (x + 4) \Rightarrow f (x - 2) = f (x + 6) f (x) = f (x + 8)$
Period is $8$