FunctionHard
Question
The domain of the function f(x) = sin-1 
+ 
+ log(3{x} + 1) (x2 + 1),
where {.} represents fractional part function, is:
+ + log(3{x} + 1) (x2 + 1),where {.} represents fractional part function, is:
Options
A.x ∈ {1}
B.x ∈ R - {1, - 1}
C.x > 3, x ≠ I
D.none of these
Solution
f(x) = sin-1 
+ 
+ log(3{x} + 1) (x2 + 1)
Domain : 3{x} + 1 ≠ 1 or 0 ⇒ x ∈ I
and - 1 ≤
≤ 1
- 2x3/2 ≤ 1 + x3 ≤ 2x3/2
1 + x3 + 2x3/2 ≥ 0
(1 + x3/2)2 ≥ 0 ⇒ x ∈ R
1 + x3 - 2x3/2 ≤ 0
or (1 - x3/2)2 ≤ 0
or 1 - x3/2 = 0 or x = 1
Hence domain x ∈ φ
+ + log(3{x} + 1) (x2 + 1)Domain : 3{x} + 1 ≠ 1 or 0 ⇒ x ∈ I
and - 1 ≤
≤ 1- 2x3/2 ≤ 1 + x3 ≤ 2x3/2
1 + x3 + 2x3/2 ≥ 0
(1 + x3/2)2 ≥ 0 ⇒ x ∈ R
1 + x3 - 2x3/2 ≤ 0
or (1 - x3/2)2 ≤ 0
or 1 - x3/2 = 0 or x = 1
Hence domain x ∈ φ
Create a free account to view solution
View Solution FreeMore Function Questions
If f(x) = loge(x + ), then f−1(x) equals-...If f(x) = and g (x) = , then common domain of function is -...Let k be a non-zero real number. If f(x) = is a continuous function, then thevalue of k is :...The graph of φ (x) is given then the number of positive solution of || φ(x)|-1| = 1 are -...Solution of (2x + 1) (x − 3) (x + 7) < 0 is-...