Question

A function T multiplies the input z by 2/3 and divides that by the quantity (z-1/2).

Answer 1

$T(z)= \frac{ \frac{2}{3} z}{z- \frac{1}{2} }$
T(3) = 2/2.5 = 4/5 or 0.8
T(1/2) is indeterminate, he reason being that the denominator becomes zero. Division by zero gives an indeterminate result.