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

Answer 1

I assume the exercise is based on the fact that you know what the graph of f(x) = lnx looks like
sketch fx) = ln x , remember x > 0

the inverse of f(x) = lnx is
h(x) = e^x

We can sketch the inverse of a function by simply reflecting it in the line y = x

suppose we have y = ln(x-2), it would simply be
f(x) translated to the right 2 units.
sketch that.
now reflect y = ln(x-2) in the line y=x and you will have g(x) = e^(x-2)