What is the domain of the function f / circ g where f (y) = / frac{4}{y-2} and g (x) = / frac{5}{3x-1}? Express it in terms of a union of intervals of real numbers.

(-∞, ⅓) ⋃ (⅓, 2) ⋃ (2, ∞)

Step-by-step explanation:

f (x) = 4 / (x - 2)

g (x) = 5 / (3x - 1)

The domain of f (x) is x ≠ 2, or (-∞, 2) ⋃ (2, ∞).

The domain of g (x) is x ≠ ⅓, or (-∞, ⅓) ⋃ (⅓, ∞).

Therefore, the domain of f (g (x)) is the overlap:

x ≠ ⅓ or 2, or (-∞, ⅓) ⋃ (⅓, 2) ⋃ (2, ∞).