A) \[-\infty <x<\infty \]
B) \[1\le x\le 4\]
C) \[4\le x\le 16\]
D) \[-1\le x\le 1\]
Correct Answer: B
Solution :
We have, \[f(x)={{\left[ {{\log }_{10}}\left( \frac{5x-{{x}^{2}}}{4} \right) \right]}^{1/2}}\] .....(i) From (i), clearly \[f(x)\] is defined for those values of x for which \[{{\log }_{10}}\left[ \frac{5x-{{x}^{2}}}{4} \right]\ge 0\] \[\Rightarrow \,\,\left( \frac{5x-{{x}^{2}}}{4} \right)\ge {{10}^{0}}\Rightarrow \left( \frac{5x-{{x}^{2}}}{4} \right)\ge 1\] \[\Rightarrow \,\,{{x}^{2}}-5x+4\le 0\Rightarrow (x-1)(x-4)\le 0\] Hence, domain of the function is \[[1,4]\] i.e. \[1\le x\le 4.\]
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