Explain how the graph of f(x) = ln x can be used to obtain the graph of g(x) = e^(x-2).

Answer 1

f^-1(x) = e^x
g(x) = f^-1(x-2)

So, reflect f(x) around the line y=x, and then shift it 2 to the right.

In the graphs at

http://www.wolframalpha.com/input/?i=plot+y%3Dln%28x%29%2C+y%3De^%28x-2%29%2C+y%3Dx%2C+y%3De^x

you can see that
f(x) is the blue curve
the green curve is f inverse
The red curve is the green curve shifted to the right