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Mathematics
Mathematics
Problem
If
f
′
′
(
x
)
=
−
f
(
x
)
f''(x) = -f(x)
f
′′
(
x
)
=
−
f
(
x
)
, where
f
(
x
)
f(x)
f
(
x
)
is a continuous double differentiable function and
g
(
x
)
=
f
′
(
x
)
g(x) = f'(x)
g
(
x
)
=
f
′
(
x
)
. If
F
(
x
)
=
{
f
(
x
2
)
}
2
+
{
g
(
x
2
)
}
2
F(x) = \left\{ f\left(\frac{x}{2}\right) \right\}^2 + \left\{ g\left(\frac{x}{2}\right) \right\}^2
F
(
x
)
=
{
f
(
2
x
)
}
2
+
{
g
(
2
x
)
}
2
and
F
(
5
)
=
5
F(5) = 5
F
(
5
)
=
5
, then
F
(
10
)
F(10)
F
(
10
)
is a. 0 b. 5 c. 10 d. 25
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