The set of all real values of x for which f(x | vedclass

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

Question

(A) For the function $f(x) = \sqrt{\frac{|x|-2}{|x|-3}}$ to be well-defined,the expression inside the square root must be non-negative and the denomin

Vedclass · Accepted Answer

$(-\infty, -3) \cup [-2, 2] \cup (3, \infty)$

Vedclass · Answer

(A) For the function $f(x) = \sqrt{\frac{|x|-2}{|x|-3}}$ to be well-defined,the expression inside the square root must be non-negative and the denominator must not be zero.So,$\frac{|x|-2}{|x|-3} \geq 0$ and $|x|-3 
eq 0$.Let $t = |x|$,where $t \geq 0$. The inequality becomes $\frac{t-2}{t-3} \geq 0$.The critical points are $t=2$ and $t=3$.Testing intervals for $t$: $1$) If $0 \leq t  0$ (e.g.,$t=1$,$\frac{-1}{-2} = 0.5 > 0$).$2$) If $2 \leq t $3$) If $t > 3$,$\frac{t-2}{t-3} > 0$ (e.g.,$t=4$,$\frac{2}{1} = 2 > 0$).Thus,the solution for $t$ is $0 \leq t \leq 2$ or $t > 3$.Substituting back $|x| = t$,we get $0 \leq |x| \leq 2$ or $|x| > 3$.$|x| \leq 2 \implies x \in [-2, 2]$.$|x| > 3 \implies x \in (-\infty, -3) \cup (3, \infty)$.Combining these,the domain is $(-\infty, -3) \cup [-2, 2] \cup (3, \infty)$.

The set of all real values of $x$ for which $f(x)=\sqrt{\frac{|x|-2}{|x|-3}}$ is a well-defined function is

Similar Questions

The range of $f(x) = \cos[x]$ for $-\frac{\pi}{4} < x < \frac{\pi}{4}$ (where $[.]$ represents the greatest integer function less than or equal to $x$) is

Range of the function $f(x) = \frac{x^2+x+2}{x^2+x+1}, x \in R$ is

The range of the function $f(x) = -\sqrt{-x^2-6x-5}$ is

Let $f(x) = \frac{1}{7 - \sin 5x}$ be a function defined on $R$. Then the range of the function $f(x)$ is equal to:

Let the range of the function $f(x) = \frac{1}{2 + \sin 3x + \cos 3x}, x \in \mathbb{R}$ be $[a, b]$. If $\alpha$ and $\beta$ are respectively the $A.M.$ and the $G.M.$ of $a$ and $b$,then $\frac{\alpha}{\beta}$ is equal to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module