SOLUTION: Let f be the function defined by f(x) = 2x + e^x. If g(x) = f^-1(x) for all x and the point (0,1) is on the graph of f, what is the value of g'(1)?

Algebra ->  Functions -> SOLUTION: Let f be the function defined by f(x) = 2x + e^x. If g(x) = f^-1(x) for all x and the point (0,1) is on the graph of f, what is the value of g'(1)?       Log On


   

Question 1025281: Let f be the function defined by f(x) = 2x + e^x. If g(x) = f^-1(x) for all x and the point (0,1) is on the graph of f, what is the value of g'(1)?

Found 2 solutions by Fombitz, robertb:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
df%2Fdx=2%2Be%5Ex
Find x when df%2Fdx=1,
2%2Be%5Ex=1
e%5Ex=-1
There is not a value for x when this will occur.
So dg%2Fdx at x=1 does not exist.

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
If y = f(x), then df%5E%28-1%29%28y%29%2Fdy+=+1%2F%28dy%2Fdx%29+=+1%2F%28df%280%29%2Fdx%29. (A statement of the inverse function theorem. f(x) is continuously differentiable at x = 0.)
Now f%28x%29+=+2x+%2B+e%5Ex ==> f'(x) = df%28x%29%2Fdx+=+2+%2B+e%5Ex+
==>