00:02
Given the function of f of x equals 2x plus 1 over x plus 3, to find the inverse think of f of x as a y, interchange x and y, and then solve for y.
00:17
We can solve for y by multiplying the quantity y plus 3 to both sides.
00:22
Distribute the x.
00:26
Sort this out so that terms with y are on the left -hand side in terms without y are on the right -hand side.
00:35
So subtract 3x, subtract 2y, factor out of y.
00:43
And then divide by the quantity x minus 2.
00:47
And that is our candidate inverse function.
00:56
To verify, compose f of f inverse of x, which would be f of 1 minus 3x over x minus 2.
01:03
Substitute that in for x into the original function.
01:07
So it would be 2 times 1 minus 3x over x minus 2 plus 1 over 1 minus 3x over x minus 2 plus 3.
01:21
Simplify.
01:28
So we have two minus six x over x minus two plus one over one minus three x over x minus two plus three...