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Question 84 - Algebra Practice | Prasnya
Q84
00:00
30 Nov 2025
Q84.
Let
f
(
x
)
=
x
2
x
−
1
f(x)=\dfrac{x}{2x-1}
f
(
x
)
=
2
x
−
1
x
and
g
(
x
)
=
x
x
−
1
g(x)=\dfrac{x}{x-1}
g
(
x
)
=
x
−
1
x
. Then, the domain of the function
h
(
x
)
=
f
(
g
(
x
)
)
+
g
(
f
(
x
)
)
h(x) = f(g(x)) + g(f(x))
h
(
x
)
=
f
(
g
(
x
))
+
g
(
f
(
x
))
is all real numbers except
A
1
2
,
1
,
and
3
2
\dfrac12, 1, \text{and } \dfrac32
2
1
,
1
,
and
2
3
B
−
1
2
,
1
2
,
and
1
-\dfrac12, \dfrac12, \text{and } 1
−
2
1
,
2
1
,
and
1
C
−
1
,
1
2
,
and
1
-1, \dfrac12, \text{and } 1
−
1
,
2
1
,
and
1
D
1
2
,
and
1
\dfrac12, \text{and } 1
2
1
,
and
1
Save
Check
Details
Q84
00:00
30 Nov 2025
Q84.
Let
f
(
x
)
=
x
2
x
−
1
f(x)=\dfrac{x}{2x-1}
f
(
x
)
=
2
x
−
1
x
and
g
(
x
)
=
x
x
−
1
g(x)=\dfrac{x}{x-1}
g
(
x
)
=
x
−
1
x
. Then, the domain of the function
h
(
x
)
=
f
(
g
(
x
)
)
+
g
(
f
(
x
)
)
h(x) = f(g(x)) + g(f(x))
h
(
x
)
=
f
(
g
(
x
))
+
g
(
f
(
x
))
is all real numbers except
A
1
2
,
1
,
and
3
2
\dfrac12, 1, \text{and } \dfrac32
2
1
,
1
,
and
2
3
B
−
1
2
,
1
2
,
and
1
-\dfrac12, \dfrac12, \text{and } 1
−
2
1
,
2
1
,
and
1
C
−
1
,
1
2
,
and
1
-1, \dfrac12, \text{and } 1
−
1
,
2
1
,
and
1
D
1
2
,
and
1
\dfrac12, \text{and } 1
2
1
,
and
1
Save
Check
Details
