Antibiotic dosage

Antibiotic dosage:Antibiotics are used to treat bacterial sinus infections.

1. If a dosage ofxmg is taken orally, suppose that the amount absorbed into the bloodstream through the stomach ish(x) =8x/x+8 mg.
2. Ifxmg enters the bloodstream, the amount surviving filtration by the liver isg(x) =1/4x.

3.Finally, ifxmg survives filtration by the liver, thenf(x) =x1mg is absorbed into the sinus cavity, provided thatx >1(otherwisef(x) = 0).

Usefunctional compositionto derive the function that relates oral dosage to the amount of drug that reaches the sinus cavity.