Question

If the function f(x)=x3+ex/2 and g(x)=f-1, then the value of g'(1) is

Answer 1

Explanation:
g(x) is the inverse of f(x)
So,g(f(x))=x
'g'(f(x))'f'(x)=1
'g'(f(x))=1f'(x)
We need to find out when f(x)=1
Clearly this happens for x=0
So g'(1)=1f'(0)
f'(x)=3x2+12el2
f'(0)=0+12=12
So g'(1)=2
Hence, the correct answer is (2).