Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
Consider function
f
(
x
)
f(x)
f
(
x
)
satisfies the relation
f
(
x
+
y
3
)
=
f
(
x
)
+
f
(
y
3
)
f(x+y^3) = f(x) + f(y^3)
f
(
x
+
y
3
)
=
f
(
x
)
+
f
(
y
3
)
,
∀
x
,
y
∈
R
\forall x, y \in R
∀
x
,
y
∈
R
and differentiable for all
x
x
x
. a. Statement I If
f
′
(
2
)
=
a
f'(2) = a
f
′
(
2
)
=
a
, then
f
′
(
−
2
)
=
a
f'(-2) = a
f
′
(
−
2
)
=
a
b. Statement II
f
(
x
)
f(x)
f
(
x
)
is an odd function.
Browse the problem library