Q59 / 90 · KVPY 2012 (SB/SX) · Mathematics

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

  • A
    $1 / 4$
  • Correct answer
    B
    $3 / 2$
  • C
    $2 / 3$
  • D
    $-2 / 5$

Solution

$\begin{array}{l} f(x)=\sqrt{4-\sqrt{2 x+5}} \\ 4-\sqrt{2 x+5} \geq 0 \quad 2 x+5 \geq 0 \\ \sqrt{2 x+5} \leq 4 \quad x \geq-5 / 2 \\ x \leq \frac{11}{2} \\ x \in\left[-\frac{5}{2}, \frac{11}{2}\right] \\ \text { mid point }=\frac{-5 / 2+11 / 2}{2}=\frac{3}{2} \end{array}$

Hence, the correct answer is option: 'B'.

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