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Mathematics
Mathematics
Problem
If
f
′
′
(
x
)
=
−
f
(
x
)
f''(x)=-f(x)
f
′′
(
x
)
=
−
f
(
x
)
and
g
(
x
)
=
f
′
(
x
)
g(x)=f'(x)
g
(
x
)
=
f
′
(
x
)
and
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 given that
F
(
5
)
=
5
F(5)=5
F
(
5
)
=
5
, then
F
(
10
)
F(10)
F
(
10
)
is (a) 5 (b) 10 (c) 0 (d) 15
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