Let y = sqrt{frac{(x + 1)(x - 3)}{(x - 2)}}. | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) For $y$ to be a real value,the expression under the square root must be non-negative:$\frac{(x + 1)(x - 3)}{(x - 2)} \ge 0$We use the sign scheme

Vedclass · Accepted Answer

$[-1, 2) \cup [3, \infty)$

Vedclass · Answer

(A) For $y$ to be a real value,the expression under the square root must be non-negative:$\frac{(x + 1)(x - 3)}{(x - 2)} \ge 0$We use the sign scheme (Wavy Curve Method) for the expression $f(x) = \frac{(x + 1)(x - 3)}{(x - 2)}$.The critical points are $x = -1, 2, 3$.Testing the intervals:$1$. For $x \in (-1, 2)$,let $x = 0$: $\frac{(1)(-3)}{(-2)} = \frac{3}{2} > 0$ (Valid).$2$. For $x \in [3, \infty)$,let $x = 4$: $\frac{(5)(1)}{(2)} = \frac{5}{2} > 0$ (Valid).$3$. At $x = -1$,$y = 0$ (Valid).$4$. At $x = 3$,$y = 0$ (Valid).$5$. At $x = 2$,the expression is undefined.Combining these,the solution is $x \in [-1, 2) \cup [3, \infty)$.

Let $y = \sqrt{\frac{(x + 1)(x - 3)}{(x - 2)}}$. Then,the set of all real values of $x$ for which $y$ takes real values is:

Similar Questions

Domain of $f(x) = (x^2 - 1)^{-1/2}$ is

If the domain of the function $\log _e\left(\frac{6 x^2+5 x+1}{2 x-1}\right)+\cos ^{-1}\left(\frac{2 x^2-3 x+4}{3 x-5}\right)$ is $(\alpha, \beta) \cup(\gamma, \delta]$,then $18\left(\alpha^2+\beta^2+\gamma^2+\delta^2\right)$ is equal to $....$.

If $f: R \to R$,then the range of the function $f(x) = \frac{x^2}{x^2 + 1}$ is

Domain of $f(x) = \frac{x}{1-|x|}$ is

If the range of the function $f(x) = \frac{5-x}{x^2-3x+2}$,$x \neq 1, 2$,is $(-\infty, \alpha] \cup [\beta, \infty)$,then $\alpha^2 + \beta^2$ is equal to :

Vedclass Test Series

Exam Paper Generator

Online Exam Module