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Many-One onto Function

If f:R → R ...

Question

If $f : R \to R$ is a function satisfying the property $f (x + 1) + f (x + 3) = 2$ for all $x \in R$ than f is

Periodic with period 3

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Periodic with period 4

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non periodic

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Periodic with period 5

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Solution

The correct option is C Periodic with period 4
$f : R \to R ∴ f (x + 1) + f (x + 3) = 2 \forall x ϵ R f o r x = 0 f (1) + f (3) = 2 - (i) f o r x = 2 f (3) + f (5) = 2 - (i i) B y s o l v i n g (i) & (i i) f (1) = f (5) ∵ f (1) = f (5) f (1) = f (1 + 4) ∴ p e r i o d o f f u n c t i o n = 4$

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Similar questions

f : R \to R

f (x + 1) + f (x + 3) = K

x \in R

f (x)

\to

ϵ

ϵ

Given f(x) defined on f: R $\to$ R is a periodic function with the fundamental period 2 then f(3) is not equal to -

f

f (x + T) = 1 + {1 - 3 f (x) + 3 (f (x))^{2} - (f (x))^{3}}^{1 / 3}

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2 T

f (x + 2 T) = f (x)

f (x)

2 T

\to

\frac{1}{2} + \sqrt{f (x) - f^{2} (x)}

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