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JEE Advanced2009MathematicsDifferentiationActual

If the function f(x)=x^3+e^ x 2 and g(x)=f⁻¹(x) , then the value of g^ (1) is

Correct answer

0

Step-by-step solution

Given, g f(x) =x array lc & g^ f(x) f^ (x)=1 If & f(x)=1 x=0, f(0)=1 array Substitute x=0 in Eq. (i), we get aligned & g^ (1)= 1 f^ (0) & g^ (1)=2 & [ f^ (x)=3 x^2+ 1 2 e^ x / 2 f^ (0)= 1 2 ] & aligned

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