00:01
In this question, they say, suppose that f of x is equal to x plus the square root of 2 minus x, and g of u is equal to u plus the square root of 2 minus u.
00:12
I want to know, is it true that f is equal to g? and i claim that the answer to this is yes, these two functions are indeed equal to each other.
00:24
To see that, let's evaluate f, for example, at negative 2.
00:31
So if i evaluated f at negative 2, everywhere i see an x, i would replace it with a negative 2.
00:39
I would get negative 2 plus the square root of 2 minus negative 2.
00:47
I would get negative 2 plus the square root of 4.
00:52
Of course, the square root of 4 is 2, so you're getting negative 2 plus 2, which is 0.
01:01
Then, i evaluate g of negative 2.
01:05
Well, what is that? everywhere i see a u, i replace it with negative 2.
01:10
So it's negative 2 plus the square root of 2 minus negative 2.
01:17
I'm getting negative 2 plus the square root of 4...