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Question 26 - Week 5 Practice | Prasnya
Q26
00:00
6 Aug 2023
Q26.
Consider the functions
f
(
x
)
=
log
x
2
f(x)=\log x^2
f
(
x
)
=
lo
g
x
2
and
g
(
x
)
=
2
x
+
1
g(x)=2x+1
g
(
x
)
=
2
x
+
1
. Which of the following options is/are true?
A
The domain of
(
f
∘
g
)
(
x
)
(f\circ g)(x)
(
f
∘
g
)
(
x
)
is
R
∖
{
−
1
2
}
\mathbb{R}\setminus\{-\frac{1}{2}\}
R
∖
{
−
2
1
}
.
B
(
f
∘
g
)
(
x
)
=
log
(
2
x
+
1
)
(f\circ g)(x)=\log(2x+1)
(
f
∘
g
)
(
x
)
=
lo
g
(
2
x
+
1
)
.
C
The domain of
(
g
∘
f
)
(
x
)
(g\circ f)(x)
(
g
∘
f
)
(
x
)
is
R
∖
{
−
1
2
}
\mathbb{R}\setminus\{-\frac{1}{2}\}
R
∖
{
−
2
1
}
.
D
(
g
∘
f
)
(
x
)
=
2
log
x
2
+
1
(g\circ f)(x)=2\log x^2+1
(
g
∘
f
)
(
x
)
=
2
lo
g
x
2
+
1
.
E
The domain of
(
g
∘
f
)
(
x
)
(g\circ f)(x)
(
g
∘
f
)
(
x
)
is
R
∖
{
0
}
\mathbb{R}\setminus\{0\}
R
∖
{
0
}
.
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Q26
00:00
6 Aug 2023
Q26.
Consider the functions
f
(
x
)
=
log
x
2
f(x)=\log x^2
f
(
x
)
=
lo
g
x
2
and
g
(
x
)
=
2
x
+
1
g(x)=2x+1
g
(
x
)
=
2
x
+
1
. Which of the following options is/are true?
A
The domain of
(
f
∘
g
)
(
x
)
(f\circ g)(x)
(
f
∘
g
)
(
x
)
is
R
∖
{
−
1
2
}
\mathbb{R}\setminus\{-\frac{1}{2}\}
R
∖
{
−
2
1
}
.
B
(
f
∘
g
)
(
x
)
=
log
(
2
x
+
1
)
(f\circ g)(x)=\log(2x+1)
(
f
∘
g
)
(
x
)
=
lo
g
(
2
x
+
1
)
.
C
The domain of
(
g
∘
f
)
(
x
)
(g\circ f)(x)
(
g
∘
f
)
(
x
)
is
R
∖
{
−
1
2
}
\mathbb{R}\setminus\{-\frac{1}{2}\}
R
∖
{
−
2
1
}
.
D
(
g
∘
f
)
(
x
)
=
2
log
x
2
+
1
(g\circ f)(x)=2\log x^2+1
(
g
∘
f
)
(
x
)
=
2
lo
g
x
2
+
1
.
E
The domain of
(
g
∘
f
)
(
x
)
(g\circ f)(x)
(
g
∘
f
)
(
x
)
is
R
∖
{
0
}
\mathbb{R}\setminus\{0\}
R
∖
{
0
}
.
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