FunctionHard
Question
The domain of the function f(x) = 
is
isOptions
A.(- 4, -3) ∪ (4, ∞)
B.(- ∞, -3) ∪ (4, ∞)
C.(- ∞, - 4) ∪ (3, ∞)
D.None
Solution
f(x) = 
For domain :
Case-I
0 <
< 1 ⇒ - 4 < x < - 2 ......A
then
⇒ log2
≥ 1
⇒
≥ 2 ⇒ x < - 3 ..........B
⇒ on A ∩ B x ∈ (-4, -3) ..........(i)
Case-II
> 1 or x > - 2 ..........A
⇒ 0 < log2
≤ 1 ⇒ 1 < 
≤ 2
⇒ x ∈ (4, ∞) ........(ii)
∴ (i) ∪ (ii) Domain x ∈ (-4, -3) ∪ (4, ∞)
For domain :
Case-I
0 <
< 1 ⇒ - 4 < x < - 2 ......Athen
⇒ log2
≥ 1⇒
≥ 2 ⇒ x < - 3 ..........B⇒ on A ∩ B x ∈ (-4, -3) ..........(i)
Case-II
> 1 or x > - 2 ..........A⇒ 0 < log2
≤ 1 ⇒ 1 < ≤ 2⇒ x ∈ (4, ∞) ........(ii)
∴ (i) ∪ (ii) Domain x ∈ (-4, -3) ∪ (4, ∞)
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