Test:
Functions I - Ambitious
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Question 1:
Which of the functions is one-to-one?
A
f
(
x
)
=
sin
x
,
{
x
:
−
π
≤
x
≤
π
}
B
f
(
x
)
=
x
2
,
{
x
∈
ℝ
}
C
f
(
x
)
=
x
2
,
{
x
:
0
≤
x
≤
+
∞
}
D
f
(
x
)
=
cos
x
,
{
x
:
−
π
2
≤
x
≤
π
2
}
Question 2:
Which of the functions is many-to-one?
A
f
(
x
)
=
sin
x
,
{
x
:
π
2
≤
x
≤
3
2
π
}
B
f
(
x
)
=
sin
x
,
{
x
:
3
2
π
<
x
<
5
2
π
}
C
f
(
x
)
=
tan
x
,
{
x
:
π
<
x
<
2
π
}
D
f
(
x
)
=
tan
x
,
{
x
:
0
≤
x
≤
π
}
Question 3:
Find the inverse of the function
f
(
x
)
=
x
2
−
3
,
x
≥
0
A
f
−
1
(
x
)
=
3
x
B
f
−
1
(
x
)
=
x
+
3
C
f
−
1
(
x
)
=
x
+
3
D
f
−
1
(
x
)
=
1
x
+
3
Question 4:
Find the inverse of the function
f
(
x
)
=
0.3
x
A
f
−
1
(
x
)
=
x
0.3
B
f
−
1
(
x
)
=
0.3
x
C
f
−
1
(
x
)
=
log
0.3
x
D
f
−
1
(
x
)
=
0.3
log
x
Question 5:
Find
g
(
f
(
3
)
)
, where
f
(
x
)
=
1
3
x
2
,
g
(
x
)
=
2
x
+
3
A
g
(
f
(
3
)
)
=
6
B
g
(
f
(
3
)
)
=
27
C
g
(
f
(
3
)
)
=
9
D
g
(
f
(
3
)
)
=
15
Question 6:
Find
g
(
f
(
3
)
)
=
15
, where
f
(
x
)
=
2
x
+
1
,
g
(
x
)
=
1
5
x
2
,
h
(
x
)
=
2
x
A
g
(
h
(
f
(
x
)
)
)
=
2
5
x
2
+
1
B
g
(
h
(
f
(
x
)
)
)
=
2
5
x
+
2
C
g
(
h
(
f
(
x
)
)
)
=
6
5
x
2
D
g
(
h
(
f
(
x
)
)
)
=
4
20
x
2
+
20
x
+
5
Question 7:
Which of the following functions is even?
A
f
(
x
)
=
e
−
x
2
B
f
(
x
)
=
x
3
+
1
C
f
(
x
)
=
sin
(
x
)
D
f
(
x
)
=
1
x
Question 8:
Which of the following functions is odd?
A
f
(
x
)
=
cos
(
x
)
B
f
(
x
)
=
2
C
f
(
x
)
=
|
x
|
D
f
(
x
)
=
x
3
Question 9:
Find the period of the function
f
(
x
)
=
sin
(
5
θ
)
A
2
π
B
3
5
π
C
5
π
D
2
5
π
Question 10:
Find the period of the function
f
(
x
)
=
tan
(
3
θ
)
A
1
3
π
B
2
3
π
C
2
π
D
π
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