A function is just a rule of associations, telling you how to deal with every (feasible) input.
In this case, writing
[tex] f(x) = \dfrac{3}{x+2}-\sqrt{x-3} [/tex]
means that, whenever a number [tex] x [/tex] is given as input, the correspondent output will be computed as the rule states: you divide 3 by that input plus two, and then you will subtract the square root of the input, minus 3.
So, if we're asked for a specific value, we have to perform this instructions, using 19 as input:
[tex] f(19) = \dfrac{3}{19+2}-\sqrt{19-3} = \dfrac{3}{21} - \sqrt{16} = \dfrac{1}{7} - 4 [/tex]
