The mid-point of the domain of the function f | vedclass

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(B) The function $f(x) = \sqrt{4 - \sqrt{2x + 5}}$ is defined if the expressions under the square roots are non-negative.First,for the inner square ro

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$\frac{3}{2}$

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(B) The function $f(x) = \sqrt{4 - \sqrt{2x + 5}}$ is defined if the expressions under the square roots are non-negative.First,for the inner square root: $2x + 5 \geq 0 \implies x \geq -\frac{5}{2}$.Second,for the outer square root: $4 - \sqrt{2x + 5} \geq 0 \implies 4 \geq \sqrt{2x + 5}$.Squaring both sides (since both are non-negative): $16 \geq 2x + 5 \implies 11 \geq 2x \implies x \leq \frac{11}{2}$.Combining these conditions,the domain of $f(x)$ is $x \in \left[ -\frac{5}{2}, \frac{11}{2} \right]$.The mid-point of the domain is calculated as $\frac{-\frac{5}{2} + \frac{11}{2}}{2} = \frac{\frac{6}{2}}{2} = \frac{3}{2}$.

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

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