let f: R ---> R+ and g: --> R+ . R be defined as f(x) = ex and g(x) = lnx.let f: R ------> R+ ...

You need to follow the steps of procedure of finding the
inverse of a function such that:

You need to substitute y
for f(x) such that:

e^x

You need to substitute y for x and x for y such
that:

You need to
solve for y the equation x = e^y, hence you should take logarithms both sides such
that:

(e^y)

You need to use power property of logarithms such
that:

You need
to remember that   such that:

y

Notice that the last line represents the
function g(x) = ln x, hence, the function g(x) expresses the inverse of function
f(x).