IIT JEE 2009 P2 Q38

If th efunction f(x) = x³+e^x/2 and g(x)=f^-1(x) then the value of g'(1) is

2 Answers

f(x) = x³ + e^x/2
f(0) = 1
f '(x) = 3x² + (1/2)e^x/2
f '(0) = 1/2

g(f(x)) = x
g'(f(x)).f '(x) = 1
g'(f(x)) = 1/f '(x)
g'(1) = g'(f(0)) = 1/f '(0) = 1/(1/2) = 2

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