Problems in Mathematical Analysis.pdf - pwp.net.ipl.pt

12 Introduction to Analysis \Ch. I
then the function x = g(y), or, in standard notation, y=g(x), is the inverse
of y = f(x). Obviously, g[f(x)]s&x, that is, the function f (x) is the inverse
of g(x) (and vice ve^sa).
In He fereia! case, the equation y f(x) defines a multiple-valued in-
verse function x = f~ }
(y) such that y ==[[(-* (y)\ for all y that are values of
the function f (x)
Lxanple 2. Determine the inverse of the function
and
Solution. Solving equation (1) for x, we have
2-*=l y
*
y=l-2-*. (1)
log(l-y)
log 2
j ' w
Obviously, the domain of
of the function
Definition
(2) is oo