The domain of the function f ( x )=( operatornamearc cot x /√ x 2-[ x 2]), where [ x ] denotes the greatest integer not greater than x, is :

Question

The domain of the function f ( x )=( operatornamearc cot x /√ x 2-[ x 2]), where [ x ] denotes the greatest integer not greater than x, is : (A) R (B) R - 0  (C) R - ± √ n: n ∈ I + ∪ 0  (D) R - n: n ∈ I

Tardigrade Admin · Accepted Answer

x2-[x2]= x2 >0 ; but 0 ≤ y <1 ⇒ x2 ≠ 0 ⇒ x ≠ ± √n

Q. The domain of the function $f (x) = \frac{arc c o t x}{x ^{2} - [ x ^{2} ]}$ , where $[x]$ denotes the greatest integer not greater than $x$ , is :

$R$

$R - {0}$

$R - {\pm n : n \in I^{+} \cup {0}}$

$R - {n : n \in I}$

$x^{2} - [x^{2}] = {x^{2}} > 0;$ but $0 \leq {y} < 1 \Rightarrow {x^{2}} \neq = 0 \Rightarrow x \neq = \pm n$

Q. The domain of the function f(x)=x2−[x2]​arccotx​, where [x] denotes the greatest integer not greater than x, is :

R

R−{0}

R−{±n​:n∈I+∪{0}}

R−{n:n∈I}

x2−[x2]={x2}>0; but 0≤{y}<1⇒{x2}=0⇒x=±n​

Q. The domain of the function $f (x) = \frac{arc c o t x}{x ^{2} - [ x ^{2} ]}$ , where $[x]$ denotes the greatest integer not greater than $x$ , is :

$R$

$R - {0}$

$R - {\pm n : n \in I^{+} \cup {0}}$

$R - {n : n \in I}$

$x^{2} - [x^{2}] = {x^{2}} > 0;$ but $0 \leq {y} < 1 \Rightarrow {x^{2}} \neq = 0 \Rightarrow x \neq = \pm n$