The mid-point of the domain of the function&n | vedclass

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Question

(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}

Vedclass · Accepted Answer

$\frac{3}{2}$

Vedclass · Answer

(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 $x \geq-5 / 2$

$	herefore$ Domain of $f(x) x \in\left[\frac{-5}{2}, \frac{11}{2}ight]$

Mid-point of domain $\frac{\frac{-5}{2}+\frac{11}{2}}{2}=\frac{3}{2}$

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

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