The domain of the function is (where [x] denotes the greatest integer less than or equal to x). [2023]

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

Q.
The domain of the function $f (x) = \frac{1}{\sqrt{{[x]}^{2} - 3 [x] - 10}}$ is (where [x] denotes the greatest integer less than or equal to x). [2023]

1 $(- \infty, - 3] \cup (5, \infty)$

2 $(- \infty, - 2) \cup [6, \infty)$

3 $(- \infty, - 3] \cup [6, \infty)$

4 $(- \infty, - 2) \cup (5, \infty)$

Ans.
(2)

${[x]}^{2} - 3 [x] - 10 > 0$

$\Rightarrow {[x]}^{2} - 5 [x] + 2 [x] - 10 > 0 \Rightarrow ([x] - 5) ([x] + 2) > 0$

$\Rightarrow [x] < - 2 or [x] > 5 \Rightarrow x < - 2 or x \geq 6$

$\Rightarrow x \in (- \infty, - 2) \cup [6, \infty)$

Solution

Q.
The domain of the function $f (x) = \frac{1}{\sqrt{{[x]}^{2} - 3 [x] - 10}}$ is (where [x] denotes the greatest integer less than or equal to x). [2023]

1 $(- \infty, - 3] \cup (5, \infty)$

2 $(- \infty, - 2) \cup [6, \infty)$

3 $(- \infty, - 3] \cup [6, \infty)$

4 $(- \infty, - 2) \cup (5, \infty)$

Ans.
(2)

${[x]}^{2} - 3 [x] - 10 > 0$

$\Rightarrow {[x]}^{2} - 5 [x] + 2 [x] - 10 > 0 \Rightarrow ([x] - 5) ([x] + 2) > 0$

$\Rightarrow [x] < - 2 or [x] > 5 \Rightarrow x < - 2 or x \geq 6$

$\Rightarrow x \in (- \infty, - 2) \cup [6, \infty)$

Want Us to Email you About Special Offers & Updates?

Solution

Q. The domain of the function f(x)=1[x]2-3[x]-10 is (where [x] denotes the greatest integer less than or equal to x). [2023]

1 (-∞,-3]∪(5,∞)

2 (-∞,-2)∪[6,∞)

3 (-∞,-3]∪[6,∞)

4 (-∞,-2)∪(5,∞)

Ans. (2) [x]2-3[x]-10>0 ⇒[x]2-5[x]+2[x]-10>0 ⇒([x]-5)([x]+2)>0 ⇒[x]<-2 or [x]>5 ⇒x<-2 or x≥6 ⇒x∈(-∞,-2)∪[6,∞)

Want Us to Email you About Special Offers & Updates?

Q.
The domain of the function $f (x) = \frac{1}{\sqrt{{[x]}^{2} - 3 [x] - 10}}$ is (where [x] denotes the greatest integer less than or equal to x). [2023]

1 $(- \infty, - 3] \cup (5, \infty)$

2 $(- \infty, - 2) \cup [6, \infty)$

3 $(- \infty, - 3] \cup [6, \infty)$

4 $(- \infty, - 2) \cup (5, \infty)$

Ans.
(2)

${[x]}^{2} - 3 [x] - 10 > 0$

$\Rightarrow {[x]}^{2} - 5 [x] + 2 [x] - 10 > 0 \Rightarrow ([x] - 5) ([x] + 2) > 0$

$\Rightarrow [x] < - 2 or [x] > 5 \Rightarrow x < - 2 or x \geq 6$

$\Rightarrow x \in (- \infty, - 2) \cup [6, \infty)$