Functions Question 374
Question: The domain of $ f(x)=\frac{1}{\sqrt{2x-1}}-\sqrt{1-x^{2}} $ is:
Options:
A) $ ] \frac{1}{2},1 [ $
B) $ [ -1,\infty [ $
C) $ [ 1,\infty [ $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Given, $ f(x)=\frac{1}{\sqrt{2x-1}}-\sqrt{1-x^{2}}=p(x)-q(x) $ Where $ p(x)=\frac{1}{\sqrt{2x-1}} $ and $ q(x)=\sqrt{1-x^{2}} $ Now, Domain of $ p(x) $ exist when $ 2x-1\ne 0 $
$ \Rightarrow x=\frac{1}{2} $ And $ 2x-1>0 $
$ \Rightarrow x=\frac{1}{2} $ And $ x>\frac{1}{2}\therefore x\in ( \frac{1}{2},\infty ) $ And domain of q(x) exists when $ 1-x^{2}\ge 0 $
$ \Rightarrow x^{2}\le 1\Rightarrow | x |\le 1\therefore -1\le x\le 1 $
$ \therefore $ Common domain is $ ] \frac{1}{2},1 [ $
BETA
