Question: A function (x, y, z) is called homogeneous of degree n if (x, y, z) = n (x, y, z) for all R.

A function ƒ(x, y, z) is called homogeneous of degree n if ƒ(λx, λy, λz) = λn ƒ(x, y, z) for all λ ∈ R.

Show that the following functions are homogeneous and determine their degree:

(a) f(x, y, z) = xy + xyz (c) f(x, y, z) = In (2) (b) f(x, y, z) = 3x + 2y = 8z (d) f(x,y, z)= z.4

(a) f(x, y, z) = xy + xyz (c) f(x, y, z) = ln (2) (b) f(x, y, z) = 3x + 2y = 8z (d) f(x, y, z) = z

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