What is the domain of f/g given f (x) = x+4 and g (x) = x-1

Answer: the domain of f/g is every real number except 1 which can be conventionally expressed as { (x, y) : x ∈ R, x ≠ 1} OR (-∞ ≤ x < 1) ∩ (1< x ≤ ∞) OR x ∈ R; x ≠ 1.

Step-by-step explanation:

since f (x) = x + 4 and g (x) = x - 1

then f/g = x + 4/x - 1

the denominator of a function cannot be zero since a fraction with a denominator of zero is undefined.

∴ x - 1 ≠ 0

the value of x when g (x) = 0 is

x - 1 = 0

x = 1

∴ x ≠ 1

Therefore the domain of f/g is every real number except 1 which can be conventionally expressed as { (x, y) : x ∈ R, x ≠ 1} OR (-∞ ≤ x < 1) ∩ (1< x ≤ ∞) OR x ∈ R; x ≠ 1.