Question 27 - Week 5 Practice | Prasnya
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Quiz 2
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Mathematics 1
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Week 5
Question 27
00:00
Est. 2 min
Marks:
+4.00
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Passage
Consider two functions
f
(
x
)
=
x
4
log
x
x
f(x)=x^{4\log_x x}
and
g
(
x
)
=
2
x
g(x)=\sqrt{2x}
in their respective domains. Let
h
(
x
)
=
(
f
∘
g
)
(
x
)
h(x)=(f\circ g)(x)
. Use this information to answer the given subquestions.
Question
Which of the following options is/are true?
Comprehension
Medium Difficulty
02 April 2023
A
Domain of the function
f
(
x
)
f(x)
is the interval
(
0
,
1
)
∪
(
1
,
∞
)
(0,1)\cup(1,\infty)
.
B
h
(
x
)
=
(
2
x
)
4
log
2
x
2
x
h(x)=(\sqrt{2x})^{4\log_{\sqrt{2x}}\sqrt{2x}}
.
C
h
(
x
)
=
(
2
x
)
4
log
x
2
x
h(x)=(\sqrt{2x})^{4\log_{\sqrt{x}}\sqrt{2x}}
.
D
Domain of the function
1
g
(
x
)
\frac{1}{\sqrt{g(x)}}
is the interval
[
0
,
∞
)
[0,\infty)
.