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Mathematics
Mathematics
Problem
Let
f
:
R
→
R
f: R \to R
f
:
R
→
R
is a function which satisfies condition
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
for all
x
,
y
∈
R
x, y \in R
x
,
y
∈
R
. If
f
(
0
)
≥
0
f(0) \ge 0
f
(
0
)
≥
0
, then a.
f
(
x
)
=
0
f(x) = 0
f
(
x
)
=
0
only b.
f
(
x
)
=
x
f(x) = x
f
(
x
)
=
x
only c.
f
(
x
)
=
0
f(x) = 0
f
(
x
)
=
0
or
x
x
x
only d.
f
(
10
)
=
10
f(10) = 10
f
(
10
)
=
10
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