A) [1, 4]
B) [1, 0]
C) [0, 5]
D) [5, 0]
Correct Answer: A
Solution :
Since, \[f(x)=\sqrt{{{\log }_{10}}\left( \frac{5x-{{x}^{2}}}{4} \right)}\] \[\therefore \,f(x)\] exists only for \[{{\log }_{10}}\left( \frac{5x-{{x}^{2}}}{4} \right)\ge 0\] \[\Rightarrow \] \[\frac{5x-{{x}^{2}}}{4}\ge 1\] \[\Rightarrow \] \[{{x}^{2}}-5x+4\le 0\] \[\Rightarrow \] \[(x-1)(x-4)\le 0\] \[\Rightarrow \] \[x\in [1,4]\]You need to login to perform this action.
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