Injective, strictly increasing and strictly decreasing functions
A function is said to be one-to-one, or injective, iff no element of the
codomain is the image of 2 (or more) distinct elements of the domain.
An injective function is called an injection.
Example: Let f be defined as f(x) = x2.
- Is f injective if the domain is N?
- Is f injective if the domain is Z?
Let f be a function whose domain and codomain are subsets of R.
f is said to be strictly incresing, if f(x) < f(y) whenever x<y;
f is said to be strictly decreasing, if f(x) > f(y) whenever x<y.
Note: Strictly increasing and strictly decreasing functions are always