Functions Question 361
Question: . Domain of the function $ f(x)={{
[ {\log_{10}}( \frac{5x-x^{2}}{4} ) ]}^{1/2}} $ is [UPSEAT 2001]
Options:
A) $ -\infty <x<\infty $
B) $ 1\le x\le 4 $
C) $ 4\le x\le 16 $
D) $ -1\le x\le 1 $
Show Answer
Answer:
Correct Answer: B
Solution:
We have $ f(x)={{[ {\log_{10}}( \frac{5x-x^{2}}{4} ) ]}^{1/2}} $ ?..(i) From (i), clearly $ f(x) $ is defined for those values of x for which $ {\log_{10}}[ \frac{5x-x^{2}}{4} ]\ge 0 $
Þ $ ( \frac{5x-x^{2}}{4} )\ge 10^{0}\Rightarrow ( \frac{5x-x^{2}}{4} )\ge 1 $
Þ $ x^{2}-5x+4\le 0 $
Þ $ (x-1)(x-4)\le 0 $ Hence domain of the function is [1, 4].
BETA
