Functions Question 520
Question: The domain of the function $ f(x)={{\sin }^{-1}}{{{(1+e^{x})}^{-1}}} $ is
[AMU 1999]
Options:
A) $ ( \frac{1}{4},\ \frac{1}{3} ) $
B) [?1, 0]
C) [0, 1]
D) [?1, 1]
Show Answer
Answer:
Correct Answer: A
Solution:
Clearly $ 0< \frac{1}{1+e^{x}}<1 $ But $ 2<e^{x}<3 $ Þ $ 3<(e^{x}+1)<4 $ Þ $ \frac{1}{4}<\frac{1}{1+e^{x}}<\frac{1}{3} $ \Domain of $ f(x)=\left( -\infty, \infty \right) $ .
BETA
