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Most Important Selected Qs for JEE AdvancedMathematicsDifferential Equations

If f(x) and g(x) be two function such that f^ (x)=2 f^ (x)-2 f(x), g(x)=f^ (x)-f(x) . Let F(x) be defined as F(x)= [f^2(x)+g^2(x) ] [f^2(-x)+g^2(-x) ] . If F(0)=1 then the value of F(1) is

Correct answer

1

Step-by-step solution

g(x)=f^ (x)-f(x) ....(1) g^ (x)=f^ (x)-2 f(x) ....(2) F^ (x)= (2 f(x) f^ (x)+2 g(x) g^ (x) ) (f^2(-x)+g^2(-x) )+ (f^2(x)+g^2(x) ) (-2 f(-x) f^ (-x)-2 g(-x) g^ (-x) ) ...(3) Using (1) and (2) in equation (3), we get F^ (x)=0 F(x) is constant function F(0)=1=F(1)

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