Functions Question 420
Question: The Domain of the function $ f(x)=\sqrt{\frac{1}{| x-2 |-(x-2)}} $ is:
Options:
A) $ ( -\infty ,2 ] $
B) $ (2,\infty ) $
C) $ (-\infty ,2) $
D) $ [2,\infty ) $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] $ | x-2 |= \begin{cases} x-2,x\ge 2 \\ 2-x,x<2 \\ \end{cases} . $
$ \Rightarrow | x-2 |-(x-2)= \begin{cases} 0,x\ge 2 \\ 4-2x,x<2 \\ \end{cases} . $
$ \Rightarrow $ Given expression is defined for $ (-\infty ,2) $
BETA
