If and and and given that

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

If f′′(x)=−f(x)f''(x)=-f(x) and g(x)=f′(x)g(x)=f'(x) and F(x)=(f(x2))2+(g(x2))2F(x)=\left(f\left(\frac{x}{2}\right)\right)^2+\left(g\left(\frac{x}{2}\right)\right)^2 and given that F(5)=5F(5)=5, then F(10)F(10) is (a) 5 (b) 10 (c) 0 (d) 15

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