Functions Question 508
Question: The domain of the function $ f(x)=\sqrt{x-x^{2}}+\sqrt{4+x}+\sqrt{4-x} $ is
[AMU 1999]
Options:
A) $ [-4,\ \infty ) $
B) [?4, 4]
C) [0, 4]
D) [0, 1]
Show Answer
Answer:
Correct Answer: D
Solution:
$ f(x)=\sqrt{x-x^{2}}+\sqrt{4+x}+\sqrt{4-x} $ Clearly $ f(x) $ is defined, if $ 4+x\ge 0 $
Þ $ x\ge -4 $ $ 4-x\ge 0 $
Þ $ x\le 4 $ $ x(1-x)\ge 0 $
Þ $ x\ge 0 $ and $ x\le 1 $ \ Domain of $ f=(-\infty ,,4]\cap [-4,,\infty )\cap [0,,1] $ $ =[0,,1] $ .
BETA
