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. $(-\infty, 1] \cup(4, \infty)$

Home » Mark (√) against the correct answer in the following: Let . Then, dom (f) – ? A. B. C. D.

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. $(-\infty, 1] \cup(4, \infty)$

CBSE | Class 12 | Functions | Maths | RS Aggarwal

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:

Option(D) is correct.
$\mathrm{f}(\mathrm{x})=\sqrt{\frac{x-1}{x+4}}$
The domain of the function can be defined for $\sqrt{\frac{x-1}{x+4}} \geq 0$
$\begin{array}{l} \Rightarrow \sqrt{\frac{x-1}{x+4}} \geq 0 \\ \Rightarrow \frac{x-1}{x+4} \geq 0 \\ \Rightarrow \mathrm{x}-1 \geq 0 \\ \Rightarrow \mathrm{x} \geq 1 \text { and } \mathrm{x} \neq 4 \end{array}$
The intersection of above two equations gives $(-\infty, 1) \cup(4, \infty)$
Thus, domain of $\mathrm{f}(\mathrm{x})$ is $(-\infty, 1) \cup(4, \infty)$