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Mathematics
Mathematics
Problem
Which one of the following function contains only one integer in its range? [Note
sgn
(
k
)
\operatorname{sgn}(k)
sgn
(
k
)
denotes the signum function of
k
k
k
.] a.
f
(
x
)
=
1
2
cos
−
1
(
1
−
x
2
1
+
x
2
)
f(x) = \frac{1}{2} \cos^{-1}\left(\frac{1-x^2}{1+x^2}\right)
f
(
x
)
=
2
1
cos
−
1
(
1
+
x
2
1
−
x
2
)
b.
g
(
x
)
=
sgn
(
x
+
1
x
)
g(x) = \operatorname{sgn}\left(x + \frac{1}{x}\right)
g
(
x
)
=
sgn
(
x
+
x
1
)
c.
h
(
x
)
=
sin
2
x
+
2
sin
x
+
2
h(x) = \sin^2 x + 2 \sin x + 2
h
(
x
)
=
sin
2
x
+
2
sin
x
+
2
d.
k
(
x
)
=
cos
−
1
(
x
2
−
2
x
+
2
)
k(x) = \cos^{-1}(x^2 - 2x + 2)
k
(
x
)
=
cos
−
1
(
x
2
−
2
x
+
2
)
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