
10. Let f : ℝ→(1, +∞ )andg:(1,+∞) →ℝbe defined as f ( x)=x
2
+ 1 and gðyÞ= y − 1
p
: Then f and g
are inverse functions of each other.
11. Let f : A → B be a function. If f has an inverse function, then f is a bijection. (This is the converse of
the statement in Example 4.2.16.)
A Little More about Functions and Sets
The definition of function relies on sets like the domai n, the codomain, and the range. So it is not surprising
to conjecture that there might be a lot of important relations between functions, sets, and their operations.
We will examine some of them.
Again, let f be a function between the sets A and B, f : A → B. The range of f is the subset ...