Answer:
[tex]f\left(7\right)=-\frac{5}{3}[/tex]
Step-by-step explanation:
Given the function
[tex]f\left(x\right)=\frac{3}{x+2}-\sqrt{x-3}[/tex]
substitute x = 7 to find f(7)
[tex]f\left(7\right)=\frac{3}{7+2}-\sqrt{7-3}[/tex]
[tex]f\left(7\right)=\frac{3}{9}-\sqrt{4}[/tex]
[tex]f\left(7\right)=\frac{1}{3}-2[/tex]
[tex]f(7)=\frac{-5}{3}[/tex]
Apply the fraction rule: [tex]\frac{-a}{b}=-\frac{a}{b}[/tex]
[tex]f\left(7\right)=-\frac{5}{3}[/tex]
Therefore,
[tex]f\left(7\right)=-\frac{5}{3}[/tex]
