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National High School Mathematics League
1989 National High School Mathematics League
2
Anti-trigonometric Function
Anti-trigonometric Function
Source: 1989 National High School Mathematics League, Exam One, Problem 2
February 25, 2020
function
Problem Statement
Range of function
f
(
x
)
=
arctan
x
+
1
2
arcsin
x
f(x)=\arctan x+\frac{1}{2}\arcsin x
f
(
x
)
=
arctan
x
+
2
1
arcsin
x
is
(A)
(
−
π
,
π
)
(B)
[
−
3
4
π
,
3
4
π
]
(C)
(
−
3
4
π
,
3
4
π
)
(D)
[
−
1
2
π
,
1
2
π
]
\text{(A)}(-\pi,\pi)\qquad\text{(B)}[-\frac{3}{4}\pi,\frac{3}{4}\pi]\qquad\text{(C)}(-\frac{3}{4}\pi,\frac{3}{4}\pi)\qquad\text{(D)}[-\frac{1}{2}\pi,\frac{1}{2}\pi]
(A)
(
−
π
,
π
)
(B)
[
−
4
3
π
,
4
3
π
]
(C)
(
−
4
3
π
,
4
3
π
)
(D)
[
−
2
1
π
,
2
1
π
]
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