questionr
Early access
Exams
Joint Entrance Examination
Mathematics
Functions
Question 138
Question 138 of 162
Medium
MCQ
The domain of \[f(x) = {{{{\log }_{(x + 1)}}(x - 2)} \over {{e^{2{{\log }_e}x}} - (2x + 3)}},x \in \mathbb{R}\] is
A
\[( - 1,\infty ) - \{ 3\} \]
B
\[\mathbb{R} - \{ - 1,3)\]
C
\[(2,\infty ) - \{ 3\} \]
D
\[\mathbb{R} - \{ 3\} \]
Check answer
Press A-D to select · Enter to check
Solutions · 1
Post your solution
Official solution
x
−
2
>
0
⇒
x
>
2
x-2>0 \Rightarrow x>2
x
−
2
>
0
⇒
x
>
2
x
+
1
>
0
⇒
x
>
−
1
\mathrm{x}+1>0 \Rightarrow \mathrm{x}>-1
x
+
1
>
0
⇒
x
>
−
1
x
+
1
≠
1
⇒
x
≠
0
x+1 \neq 1 \Rightarrow x \neq 0
x
+
1
=
1
⇒
x
=
0
and
x
>
0
x>0
x
>
0
Denominator
x
2
−
2
x
−
3
≠
0
\mathrm{x}^{2}-2 \mathrm{x}-3 \neq 0
x
2
−
2
x
−
3
=
0
(
x
−
3
)
(
x
+
1
)
≠
0
(x-3)(x+1) \neq 0
(
x
−
3
)
(
x
+
1
)
=
0
x
≠
−
1
,
3
\mathrm{x} \neq-1,3
x
=
−
1
,
3
So Ans
(
2
,
∞
)
−
{
3
}
(2, \infty)-\{3\}
(
2
,
∞
)
−
{
3
}
Answer the question to unlock
Previous
Next