Answer:
see below
Step-by-step explanation:
[tex](f-g)(x)=f(x)-g(x)=\dfrac{2x+6}{3x}-\dfrac{\sqrt{x}-8}{3x}\\\\=\dfrac{2x+6-(\sqrt{x}-8)}{3x}=\dfrac{2x-\sqrt{x}+14}{3x}[/tex]
The difference function is the difference of the functions. Since both have the same denominator, the numerator of the difference is the difference of numerators. When -8 is subtracted, it is the same as adding 8, so the numerator of the difference will have the constant 6+8 = 14. Only one choice matches.
