Let [x] denote the greatest integer less than or equal to x. Then the domain of f(x) = sec

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

JEE MAIN
Class XI-XII
MATHEMATICS

Q.
Let [x] denote the greatest integer less than or equal to x. Then the domain of f(x) = $\sec^{- 1}$ (2[x] + 1) is : [2025]

1 $(- \infty, \infty)$

2 $(- \infty, \infty) - {0}$

3 $(- \infty, - 1] \cup [0, \infty)$

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

Ans.
(1)

We have, $2 [x] + 1 \leq - 1 or 2 [x] + 1 \geq 1$

$\Rightarrow [x] \leq - 1 or [x] \geq 0$

$\Rightarrow x \in (- \infty, 0) or x \in [0, \infty)$

$\Rightarrow x \in (- \infty, \infty)$

Solution

Q.
Let [x] denote the greatest integer less than or equal to x. Then the domain of f(x) = $\sec^{- 1}$ (2[x] + 1) is : [2025]

1 $(- \infty, \infty)$

2 $(- \infty, \infty) - {0}$

3 $(- \infty, - 1] \cup [0, \infty)$

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

Ans.
(1)

We have, $2 [x] + 1 \leq - 1 or 2 [x] + 1 \geq 1$

$\Rightarrow [x] \leq - 1 or [x] \geq 0$

$\Rightarrow x \in (- \infty, 0) or x \in [0, \infty)$

$\Rightarrow x \in (- \infty, \infty)$

Want Us to Email you About Special Offers & Updates?

Solution

Q. Let [x] denote the greatest integer less than or equal to x. Then the domain of f(x) = sec–1(2[x] + 1) is : [2025]

1 (–∞,∞)

2 (–∞,∞)–{0}

3 (–∞,–1]∪[0,∞)

4 (–∞,–1]∪[1,∞)

Ans. (1) We have, 2[x]+1≤–1 or 2[x]+1≥1 ⇒ [x]≤–1 or [x]≥0 ⇒ x∈(–∞,0) or x∈[0,∞) ⇒ x∈(–∞,∞)

Want Us to Email you About Special Offers & Updates?

Q.
Let [x] denote the greatest integer less than or equal to x. Then the domain of f(x) = $\sec^{- 1}$ (2[x] + 1) is : [2025]

1 $(- \infty, \infty)$

2 $(- \infty, \infty) - {0}$

3 $(- \infty, - 1] \cup [0, \infty)$

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

Ans.
(1)

We have, $2 [x] + 1 \leq - 1 or 2 [x] + 1 \geq 1$

$\Rightarrow [x] \leq - 1 or [x] \geq 0$

$\Rightarrow x \in (- \infty, 0) or x \in [0, \infty)$

$\Rightarrow x \in (- \infty, \infty)$