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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
x
2
−
2
x
f(x) = x^2 - 2x
f
(
x
)
=
x
2
−
2
x
,
x
∈
R
x \in \mathbb{R}
x
∈
R
and
g
(
x
)
=
f
(
f
(
x
)
−
1
)
+
f
(
5
−
f
(
x
)
)
g(x) = f(f(x) - 1) + f(5 - f(x))
g
(
x
)
=
f
(
f
(
x
)
−
1
)
+
f
(
5
−
f
(
x
))
, show that
g
(
x
)
≥
0
g(x) \ge 0
g
(
x
)
≥
0
,
∀
x
∈
R
\forall x \in \mathbb{R}
∀
x
∈
R
.
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