To find the value of [tex]\( f(7) \)[/tex] where the function [tex]\( f(x) = \frac{3}{x + 2} - \sqrt{x - 3} \)[/tex], follow these steps:
1. Evaluate the first part of the function: [tex]\( \frac{3}{x + 2} \)[/tex]
Substitute [tex]\( x = 7 \)[/tex] into the expression:
[tex]\[
\frac{3}{7 + 2} = \frac{3}{9} = \frac{1}{3}
\][/tex]
2. Evaluate the second part of the function: [tex]\( \sqrt{x - 3} \)[/tex]
Substitute [tex]\( x = 7 \)[/tex] into the expression:
[tex]\[
\sqrt{7 - 3} = \sqrt{4} = 2
\][/tex]
3. Combine the results:
[tex]\[
f(7) = \frac{1}{3} - 2
\][/tex]
4. Simplify the result:
[tex]\[
f(7) = \frac{1}{3} - 2 = \frac{1}{3} - \frac{6}{3} = \frac{1 - 6}{3} = \frac{-5}{3} = -1.6666666666666667
\][/tex]
5. Round the result to the nearest hundredth:
[tex]\[
f(7) \approx -1.67
\][/tex]
So, the completed statement is:
[tex]\[
f(7) = -1.67
\][/tex]
