consider the function f(x)=(x-1)^2+2
1. Determine the inverse of f(x)
2. Determine the domain and range of f(x) and its inverse f^-1(x)
Strictly speaking does NOT have an inverse because it is not a "one to one" function.
Yes, you can recognize that the graph of y= f(x) has a vertex at (1, 2) and then break it into TWO functions:
with domain which then has range and write or
with domain which also has range and write .
But neither of those functions is f(x) so, strictly speaking, neither of those is the inverse of f.