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Silk Road
2018 Silk Road
2
2
Part of
2018 Silk Road
Problems
(1)
f (x+1 )=1+f(x) and f (x^4-x^2 )=f^4(x)-f^2(x)
Source: SRMC 2018 P2
9/1/2018
Find all functions
f
:
R
→
R
f:\ \mathbb{R}\rightarrow\mathbb{R}
f
:
R
→
R
such that for any real number
x
x
x
the equalities are true:
f
(
x
+
1
)
=
1
+
f
(
x
)
f\left(x+1\right)=1+f(x)
f
(
x
+
1
)
=
1
+
f
(
x
)
and
f
(
x
4
−
x
2
)
=
f
4
(
x
)
−
f
2
(
x
)
.
f\left(x^4-x^2\right)=f^4(x)-f^2(x).
f
(
x
4
−
x
2
)
=
f
4
(
x
)
−
f
2
(
x
)
.
[url=http://matol.kz/comments/3373/show]source
functional equation
algebra