F- - is a function satisfying the propertyf2x-3-f2x-7-2 - x- then the fundamental period of fx is

Put 2x+3=t in the given equation. ⇒ f(t)+f(t+4)=2 …(1) nbsp; Now replace t→ t+4 f(t+4)+f(t+8)=2 …(2) From (1) (2) ⇒ f(t) f(t+8)=0 ⇒ f(t)=f(t+8) Clearly, T ...

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Standard XII

Mathematics

Trigonometric Ratios of Allied Angles

f:ℝ →ℝ is a f...

Question

$f : R \to R$ is a function satisfying the property
$f (2 x + 3) + f (2 x + 7) = 2 \forall x \in R,$ then the fundamental period of $f (x)$ is

2

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8

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12

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Solution

The correct option is C $8$
Put $2 x + 3 = t$ in the given equation.
$\Rightarrow f (t) + f (t + 4) = 2 \dots (1)$
Now replace $t \to t + 4$
$f (t + 4) + f (t + 8) = 2 \dots (2)$
From $(1) - (2)$
$\Rightarrow f (t) - f (t + 8) = 0$
$\Rightarrow f (t) = f (t + 8)$
Clearly, The fundamental period is $8.$

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Trigonometric Ratios of Allied Angles

Standard XII Mathematics

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f:R→R is a function satisfying the property f(2x+3)+f(2x+7)=2 ∀ x∈R, then the fundamental period of f(x) is

The correct option is C 8Put 2x+3=t in the given equation. ⇒f(t)+f(t+4)=2 …(1) Now replace t→t+4 f(t+4)+f(t+8)=2 …(2) From (1)−(2) ⇒f(t)−f(t+8)=0 ⇒f(t)=f(t+8) Clearly, The fundamental period is 8.

$f : R \to R$ is a function satisfying the property
$f (2 x + 3) + f (2 x + 7) = 2 \forall x \in R,$ then the fundamental period of $f (x)$ is