Since we have a table for the function, every time we have a value for x, we look for it on the x column and the f(x) value will be the value in the samr row on the f(x) column.
Similarly, if we have a value of f(x), we look for it in the column f(x) and get the corresponding x.
So, if we have f(x) = 1, we see that this value is in the 7th row, and the corresponding x is 6, so x = 6.
For f⁻¹(x) we do the same but switching the columns.
So, to find f⁻¹(9), we would normally look for x = 9, but since it is f⁻¹ we look for f(x) = 9, which is in the 6th row and the corresponding x is 5, so f⁻¹(9) = 5.
For f⁻¹(x) = 6, we would look for 6 on f(x), but since it is f⁻¹ we look for x = 6, which is in the 7th row and the corresponding f(x) is 1 so x = 1.