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Question 4 - Week 5 Practice | Prasnya
Q4
00:00
16 Mar 2025
Q4.
Let functions
f
(
x
)
=
log
(
x
2
)
f(x)=\log(x^2)
f
(
x
)
=
lo
g
(
x
2
)
,
g
(
x
)
=
2
log
x
g(x)=2\log x
g
(
x
)
=
2
lo
g
x
, and
h
(
x
)
=
(
log
x
)
2
h(x)=(\log x)^2
h
(
x
)
=
(
lo
g
x
)
2
respectively. Choose the set of correct options.
A
f
(
g
(
x
)
)
f(g(x))
f
(
g
(
x
))
is not an injective function in its domain.
B
The domain of
f
(
x
)
f(x)
f
(
x
)
and
g
(
x
)
g(x)
g
(
x
)
are equal.
C
f
(
g
(
x
)
)
f(g(x))
f
(
g
(
x
))
is an injective function in its domain.
D
The range of
h
(
x
)
h(x)
h
(
x
)
and
g
(
x
)
g(x)
g
(
x
)
are equal.
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Details
Q4
00:00
16 Mar 2025
Q4.
Let functions
f
(
x
)
=
log
(
x
2
)
f(x)=\log(x^2)
f
(
x
)
=
lo
g
(
x
2
)
,
g
(
x
)
=
2
log
x
g(x)=2\log x
g
(
x
)
=
2
lo
g
x
, and
h
(
x
)
=
(
log
x
)
2
h(x)=(\log x)^2
h
(
x
)
=
(
lo
g
x
)
2
respectively. Choose the set of correct options.
A
f
(
g
(
x
)
)
f(g(x))
f
(
g
(
x
))
is not an injective function in its domain.
B
The domain of
f
(
x
)
f(x)
f
(
x
)
and
g
(
x
)
g(x)
g
(
x
)
are equal.
C
f
(
g
(
x
)
)
f(g(x))
f
(
g
(
x
))
is an injective function in its domain.
D
The range of
h
(
x
)
h(x)
h
(
x
)
and
g
(
x
)
g(x)
g
(
x
)
are equal.
Save
Check
Details
