A) \[-\infty <x<\infty \]
B) \[1\le x\le 4\]
C) \[4\le x\le 16\]
D) \[-1\le x\le 3\]
Correct Answer: B
Solution :
[b] We have \[f(x)={{\left[ {{\log }_{10}}\left( \frac{5x-{{x}^{2}}}{4} \right) \right]}^{1/2}}\]...(1) From (1), clearly, \[f(x)\]is defined for those values of x for which \[\log \left[ \frac{5x-{{x}^{2}}}{4} \right]\ge 0\] Or \[\left( \frac{5x-{{x}^{2}}}{4} \right)\ge 10{}^\circ \] Or \[\left( \frac{5x-{{x}^{2}}}{4} \right)\ge 1\] Or \[{{x}^{2}}-5x+4\le 0\] Or \[(x-1)(x-4)\le 0\] Hence, the domain of the functions is [1, 4].
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