A) \[[-1,\,\,3]\]
B) \[(-1,\,\,3]\]
C) \[[-1,\,\,3)\]
D) None of these
Correct Answer: A
Solution :
We have, the function \[f(x)=\sqrt{3-x}+{{\cos }^{-1}}\left( \frac{3-2x}{5} \right)\] For it's existence, \[3-x\ge 0\Rightarrow x\le 3\] ... (i) and \[-1\le \frac{3-2x}{5}\le 1\] \[\Rightarrow \] \[-5\le 3-2x\le 5\] \[\Rightarrow \] \[-8\le -2x\le 2\] \[\Rightarrow \] \[-1\le x\le 4\] ... (ii) From Eqs. (i) and (ii), it is clear that the domain of the given function \[f\] is \[(-\infty ,\,\,3]\cap [-1,\,\,-4]=[-1,\,\,3]\]
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