Derivatives

[vnsin]

The question asks

If f(X) = x+2e^x, find the value of g'(1+2e), where g(x) = inverse of f(x) for all x

I have no idea where to start. I tried to find the inverse of f(x) but that only led to x=y+2e^y and I'm stuck there.

Please help.

 

[Deleted member 4993]

The question asks

If f(X) = x+2e^x, find the value of g'(1+2e), where g(x) = inverse of f(x) for all x

I have no idea where to start. I tried to find the inverse of f(x) but that only led to x=y+2e^y and I'm stuck there.

Please help.

The 'y' in the inverse function is 'g'.

then you have

x = g + 2e^g

By observation, at x = 1 + 2e ? g = 1 or g(1+2e) = 1

1 = g' + 2*g' * e^g = g' * (1+2e^g)

g' = 1/(1+ 2e^g)

Now continue....