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← IIT-JEE 2009 · Paper 2
MathematicsInteger+4 / -1Question 38 of 57

IIT-JEE 2009 · Paper 2, Mathematics question 38

If the function f(x)=x3+ex2f(x)=x^3+e^{\frac x2} and g(x)=f−1(x)g(x)=f^{-1}(x), then the value of g′(1)g'(1) is

Answer and worked solution

Official answer: 2

Inverse. f(0)=0+e0=1f(0)=0+e^0=1, so g(1)=0g(1)=0.

Derivative. g′(1)=1f′(0)=10+12e0=2g'(1)=\dfrac1{f'(0)}=\dfrac1{0+\frac12e^0}=2.

Answer: 2

Topics:Derivatives of standard functionsComposition and inverse functions
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