Relations Question 14
Question: The domain of the function $ f(x)={{[ {\log _{10}}( \frac{5x-x^{2}}{4} ) ]}^{1/2}} $ is
Options:
A) $ -\infty <x<\infty $
B) $ 1\le x\le 4 $
C) $ 4\le x\le 16 $
D) $ -1\le x\le 3 $
Show Answer
Answer:
Correct Answer: B
Solution:
We have $ f(x)={{[ {\log _{10}}( \frac{5x-x^{2}}{4} ) ]}^{1/2}} $ …(1)
From (1), clearly, $ f(x) $ is defined for those values of x for which $ \log [ \frac{5x-x^{2}}{4} ]\ge 0 $
Or $ ( \frac{5x-x^{2}}{4} )\ge 10{}^\circ $ Or $ ( \frac{5x-x^{2}}{4} )\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].
BETA
