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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
sin
x
f(x)=\sin x
f
(
x
)
=
sin
x
and
g
(
x
)
=
x
2
g(x)=\dfrac{x}{2}
g
(
x
)
=
2
x
on the interval
(
0
,
4
)
(0,4)
(
0
,
4
)
. How many distinct real numbers in
(
0
,
4
)
(0,4)
(
0
,
4
)
satisfy
f
(
x
)
=
g
(
x
)
f(x)=g(x)
f
(
x
)
=
g
(
x
)
? Justify your answer with sign considerations.
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