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
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