Mid-point of domain of function f(x)=√{4-√{2 x+5}} real x is

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1.Relation and Function

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The mid-point of the domain of the function $f(x)=\sqrt{4-\sqrt{2 x+5}}$ real $x$ is

A

$\frac{1}{4}$

B

$\frac{3}{2}$

C

$\frac{2}{3}$

D

$-\frac{2}{5}$

(KVPY-2012)

Solution

(b)

We have, $f(x)=\sqrt{4-\sqrt{2 x+5}}$

$f(x)$ is defined if

$4-\sqrt{2 x+5} \geq 0$ and $2 x+5 \geq 0$

$\Rightarrow 4 \geq \sqrt{2 x+5}$ and $x \geq-5 / 2$

$\Rightarrow 16 \geq 2 x+5$ and $x \geq-5 / 2$

$\Rightarrow x \leq \frac{11}{2}$ and $x \geq-5 / 2$

$\therefore$ Domain of $f(x) x \in\left[\frac{-5}{2}, \frac{11}{2}\right]$

Mid-point of domain $\frac{\frac{-5}{2}+\frac{11}{2}}{2}=\frac{3}{2}$

Standard 12

Mathematics

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