0:00
Hi.
00:02
In this video, we're answering the question of whether the function f of n equals 4n squared plus 1 is injective.
00:11
So it's a pretty simple question, right? so injective means that if f of n equals f of m, then n equals m.
00:28
So either the function is injective in which case this holds.
00:32
So this is the definition of the or we can find a counter example, so of two numbers and an m that are not the same, let's touch that f and n, fn equals f m.
00:49
So the key here is that we have an n squared, and you might start seeing this a lot where if you have a square, for instance, the function f of n equals n squared is not injective because f of n is negative because f of negative n is equal to f of n, right? because the square gets rid of the negative.
01:17
So we have negative n squared is equal to n squared.
01:22
And this, of course, is just equal to n squared...