question_answer

The domain of the function \[f(x)=\exp (\sqrt{5x-3-2{{x}^{2}}})\] is  [MP PET 2004]           

A)            \[\left[ 1,\ -\frac{3}{2} \right]\]

B)             \[\left[ \frac{3}{2},\ \infty  \right]\]

C)            \[[-\infty ,\ 1]\]

D)            \[\left[ 1,\ \frac{3}{2} \right]\]

Correct Answer: D

Solution :

           \[f(x)={{e}^{\sqrt{5x-3-2{{x}^{2}}}}}\]Þ\[5x-3-2{{x}^{2}}\ge 0\]or \[(x-1)\left( x-\frac{3}{2} \right)\ge 0\]            \ \[D\in \,[1,\,3/2]\].