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Question

If f'(x)=g(x) and g'(x)=f(x)for all x andf(2)=4=f'(2), then f2(4)+g2(4) is equal to


A

8

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B

16

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C

32

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D

64

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Solution

The correct option is A

8


Explanation for the correct option:

Find the value of f2(4)+g2(4):

Given that,

f'(x)=g(x)

g'(x)=f(x)

Let us consider r(x)=f2(x)+g2(x)

Differentiating r(x) with respect to x we get,

r'(x)=2f(x)f'(x)+2g(x)g'(x)=2f(x)g(x)+2g(x)(-f(x))=0

Since, r'x=0

r(x)=constantr(4)=r(2)r(2)=f2(2)+f'2(2)=22+22=8

r2=r4=8

Hence, the correct option is A.


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