If f(x) be a function satisfying the condition that f(x) = 1 3 [ … - Vidyadip

MCQ

If $f(x)$ be a function satisfying the condition that $f(x) = \frac{1}{3}\left[ {f(x + 6) + \frac{6}{{f(x + 7)}}} \right]$ and $f(x) \geq 0$ for all $x \in R$ .If $\mathop {\lim }\limits_{x \to \infty } f(x) = \sqrt m $ then value of $m$ is

✓
$3$
B
$4$
C
$6$
D
$5$

✓

Answer

Correct option: A.

$3$

a
$f(x)=\frac{f(x+6)}{3}=\frac{2}{f(x+7)}$

$\mathop {\lim }\limits_{x \to \infty } f(x) = \sqrt m = \frac{{\sqrt {3m} }}{3} + \frac{2}{{\sqrt 3 }}$

$m = \frac{m}{3} + 2$

So, $m = 3$

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