Functions 2

(CAT 2000)

For three distinct real numbers x, y and z, let
f(x, y, z) = Min(Max(x, y), Max(y, z), Max(z, x))
g(x, y, z) = Max(Min(x, y), Min(y, z), Min(z, x))
h(x, y, z) = Max(Max(x, y), Max(y, z), Max(z, x))
j(x, y, z) = Min(Min(x, y), Min(y, z), Min(z, x))
m(x, y, z) = Max(x, y, z)
n(x, y, z) = Min(x, y, z)

1. Which of the following is necessarily greater than 1?
a. [h(x, y, z) – f(x, y, z)] / j(x, y, z)
b. j(x, y, z) / h(x, y, z)
c. f(x, y, z) / g(x, y, z)
d. [f(x, y, z) + h(x, y, z) – g(x, y, z)] / j(x, y, z)

2. Which of the following expressions is necessarily equal to 1?
a. [f(x, y, z) – m(x, y, z)] / [g(x, y, z) – h(x, y, z)]
b. [m(x, y, z) – f(x, y, z)] / [g(x, y, z) – n(x, y, z)]
c. [j(x, y, z) – g(x, y, z)] / h(x, y, z)
d. [f(x, y, z) – h(x, y ,z)] / f(x, y, z)

3. Which of the following expressions is indeterminate?
a. [f(x, y, z) – h(x, y, z)] / [g(x, y, z) – j(x, y, z)]
b. [f(x, y, z) + h(x, y, z) + g(x, y, z) + j(x, y, z)] / [j(x, y, z) + h(x, y, z) – m(x, y, z) – n(x, y, z)]
c. [g(x, y, z) – j(x, y, z)] / [f(x, y, z) – h(x, y, z)]
d. [h(x, y, z) – f(x, y, z)] / [n(x, y, z) – g(x, y, z)

For answers click here.