Question:
Mark (√) against the correct answer in the following:
Let $f(x) \sqrt{\frac{x-1}{x+4}}$. Then, dom (f) - ?
A. $[1,4)$
B. $[1,4]$
C. $(-\infty, 4]$
D. $(-\infty, 1] \cup(4, \infty)$
Solution:
$f(x)=\sqrt{\frac{x-1}{x-4}}$
$\sqrt{\frac{x-1}{x-4}} \geq 0$
$\Rightarrow x-1 \geq 0$
$\Rightarrow x \geq 1$
And $x \neq 4$
$x>4$ and $x \leq 1$
$\Rightarrow \operatorname{dom}(f)=(-\infty, 1] \cup(4, \infty)$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.