The expression f(19) tells us to plug in "19" as the value of x in the f(x) function.
![\begin{gathered} f(x)=(3)/(x+2)-\sqrt[]{x-3} \\ f(19)=(3)/(19+2)-\sqrt[]{19-3} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/xq1zmo76ps9eqjkiczjsip2adhx3cbir03.png)
Then, simplify.
a. Add the denominator and subtract the numbers inside the parenthesis.
![f(19)=(3)/(21)-\sqrt[]{16}](https://img.qammunity.org/2023/formulas/mathematics/college/b7o5oy57k0vb83qh3rm9bohsx04szpe4p6.png)
b. Get the square root of 16.

c. Subtract the two numbers.

Therefore, f(19) = -27/7.