00:01
We are given a function h of x equal to 1 plus cosine x, and we are asked to find whether h of x is 1 to 1.
00:10
Or in other words, is h of x injective? so really quickly, it should be noted that the domain of h is all real numbers, and the range of age is also on real numbers.
00:25
And so if it is true that this function is injective, then for any two real numbers, a and b, if h of a is equal to h of b, then it is necessarily true that a is equal to b.
00:49
If this function is injective, then, then, you know, this is the definition right here.
00:54
If it is false, if it is not injective, then there should exist an a and b such that for, that it is true that h of a is equal to h of b.
01:11
But a is not necessarily equal to b.
01:18
So for a function like 1 plus cosine x, it's fairly straightforward to graph, and so we can use a horizontal line test to determine whether or not there exists a counter example, essentially...