The notation f:S→T denotes that f is a function, also called a map , defined on all of a set S and whose outputs lie in a set T . A function f:S→T is injective if for all x, y∈S , f(x)=f(y) implies that x=y . Alternatively: a function is injective if we can uniquely recover some input x based on an output f(x) . What functions are injective?

There are many. Two examples are

Step-by-step explanation:

There are many examples. The simplest is

1 -

It is trivial that

2 -

That function is injective as well.

An example of a function that is NOT injective is

Notice that

the answer is; biodiversity resulting from few ancestors

adaptive radiation occurs when a population is subjected to a large natural environment with spatial ecological variations. the parts of the population in the different ecologies begin to adapt to their local environments. due to non-random mating across the large populations, this causes the different populations from the large population to speciate within their local environments. they, therefore, diverge to different species sharing a common ancestor.