Matthew

Let f, g be real functions given by f(x) = 3x+2 / 2x+3

and g(x) = 1/x

State the domains of f and g and show that (f ◦ g)(x) = (g ◦ f)(x) showing all steps.

The concentration C of a drug in the blood-stream after a time t since it was administered

is found to be inversely proportional to

ln(5 + t).

Express C as a function of t and determine the constant of proportionality given that

C = 7 μg/ml at t = 0 hours. Give your answer accurate to 2 decimal places. All steps must be shown.

38. The vapour pressures of pure liquids A and B are 600 mm Hg and 100 mm Hg respectively. It follows that above an ideal solution of A in B, where the mole fraction of A is 0.300 in the liquid phase, the mole fraction of B in the vapour phase is:

(a) 0.700

(b) 0.280

(c) 0.389

(d) 0.300

(e) 0.167