Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
Let
f
(
x
)
=
a
x
17
+
b
sin
x
sin
2
x
⋅
sin
3
x
+
c
x
2
sin
(
sin
x
)
f(x) = ax^{17} + b \sin x \sin 2x \cdot \sin 3x + cx^2 \sin(\sin x)
f
(
x
)
=
a
x
17
+
b
sin
x
sin
2
x
⋅
sin
3
x
+
c
x
2
sin
(
sin
x
)
+
d
log
(
x
+
1
+
x
2
)
+
x
(
∣
x
+
1
∣
−
∣
x
−
1
∣
)
×
(
e
x
−
e
−
x
e
x
+
e
−
x
)
+ d \log(x + \sqrt{1+x^2}) + x(|x+1| - |x-1|) \times \left( \frac{e^x - e^{-x}}{e^x + e^{-x}} \right)
+
d
lo
g
(
x
+
1
+
x
2
)
+
x
(
∣
x
+
1∣
−
∣
x
−
1∣
)
×
(
e
x
+
e
−
x
e
x
−
e
−
x
)
be defined on the set of real numbers (
a
>
0
,
b
,
c
,
d
∈
R
a > 0, b, c, d \in \mathbb{R}
a
>
0
,
b
,
c
,
d
∈
R
). If
f
(
−
7
)
=
7
,
f
(
−
5
)
=
−
5
,
f
(
−
2
)
=
3
f(-7) = 7, f(-5) = -5, f(-2) = 3
f
(
−
7
)
=
7
,
f
(
−
5
)
=
−
5
,
f
(
−
2
)
=
3
, then the minimum number of zeroes of the equation
f
(
x
)
=
0
f(x) = 0
f
(
x
)
=
0
is equal to.
Browse the problem library