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Question

If F(x)=(f(x2))2+(g(x2))2 where fā€²(x)=āˆ’f(x) and g(x)=fā€²(x) and given that F(5)=5, then F(10) is equal to


A

5

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B

10

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C

0

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D

15

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Solution

The correct option is A

5


F(x)=(f(x2)2)+(g(x2))2
F(x)=2f(x2).f(x2).12+2g(x2).g(x2).12
=f(x2).f(x2)+f(x2).f(x2)
[g(x)=f(x)g(x)=f"(x)]
=f(x2).f(x2)f(x2)f(x2)
=0 [f(x)=f(x)]
F(x) is a constant fucntion.
F(x)=F(5)=5 xRF(10)=5


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