If f - R - R is a function satisfying the functional relation f 2 x -3- f 2 x -7-2- - x - R then period of f x isA- 2B- 4C- 8D- 16

The correct option is D 16f(2x+3)+f(2x+7)=2 → (1) Replace x by x + 1 ⇒ f(2x+5)+f(2x+9)=2 Replace x by x+2 → f(2x+7)+f(2x+11)=2 → (2) (1) (2) ⇒ f(2x+3) = f( ...

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Standard XII

Mathematics

Many-One onto Function

If f : R → R ...

Question

If f: R $\to$ R is a function satisfying the functional relation $f (2 x + 3) + f (2 x + 7) = 2, \forall x ϵ R$ then period of f(x) is

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Solution

The correct option is D 16
$f (2 x + 3) + f (2 x + 7) = 2 \to (1)$
Replace $x b y x + 1 \Rightarrow f (2 x + 5) + f (2 x + 9) = 2$
Replace $x b y x + 2 \to f (2 x + 7) + f (2 x + 11) = 2 \to (2)$
$(1) - (2) \Rightarrow f (2 x + 3) = f (2 x + 11)$
$∴$ period of f(2x) is 8, hence period of f(x) will be 16
$∴$ period = 16

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If f: R → R is a function satisfying the functional relation f(2x+3)+f(2x+7)=2,∀xϵR then period of f(x) is

The correct option is D 16f(2x+3)+f(2x+7)=2→(1) Replace x by x+1⇒f(2x+5)+f(2x+9)=2 Replace x by x+2→f(2x+7)+f(2x+11)=2→(2) (1)−(2)⇒f(2x+3)=f(2x+11) ∴ period of f(2x) is 8, hence period of f(x) will be 16 ∴ period = 16

If f: R $\to$ R is a function satisfying the functional relation $f (2 x + 3) + f (2 x + 7) = 2, \forall x ϵ R$ then period of f(x) is