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Let f be the real valued differentiable function on R such that e^(-x)f(x)=3/(e^(2))+4e^(-x) int_(2)^(x) sqrt(2t^(2)+6t+5)dt AA x in R and let g(x)=f^(-1) (x) then [g^(')(3)]+[|g^('')(3)|] is equal to _____ (where [.] denote the greatest integer function)

Answer»


Solution :`g(f(X))=x`
So, `g^(')(f(x)).f^(')(x)=1`
`g^('')=(f(x))=-(f^('')(x))/((f^(')(x))^(3))`
So, `g^(')(3)=1/23` and `g^('')(3)=(-43)/(5(23)^(3))`


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