If the functions f and g satisfy two conditions:. Section 4.1: Inverses. g(f(x)) = x for every x in the domain of f . f(g(x)) = x for every x in the domain of g. then f and g are inverse functions . f is an inverse of g and g is an inverse of f. Determine whether f and g are inverses:.
A function f has an inverse if and only if its graph is cut at most once by any horizontal line:
A function which passes the vertical and horizontal line tests has an inverse and is one-to-one.
If the graph of f is always increasing or decreasing, then the function f has an inverse.
How can we show a function is always increasing or decreasing?
The domain of the original is the range of the inverse. The range of the original is the domain of the inverse.