00:01
If we have the function f of x equals 1 over x minus 1, and the g function x plus 1 over x, then we want to show the composition f of g of x and g of x, and show that they simplify to x in each direction.
00:26
Therefore they are inverses of each other.
00:28
So first, plugging the g function into the f function would look like 1 over, and instead of x minus 1, it would be x plus 1 over x minus 1.
00:43
A little algebra here.
00:46
Get common denominators in the overall denominator.
00:50
So times x over x, then we have 1 over x plus 1 minus x over x.
01:02
Again, adding the numerators x plus 1, and then that's a negative x, all over the common denominator, now the positive and negative x would cancel and we have 1 over 1 over x...