Find the domain and the domain of the function: y = 2 + 4 / x-3.

The function f is given by the formula: y = 2 + 4 / (x – 3).

The domain of the function is: D (f) = R \ {3}, since for x = 3 the expression with the variable x does not make sense (you cannot divide by 0).

Function range: E (f) = R \ {2}.

x0 is expressed in terms of y0.

y0 = 2 + 4 / (x0 – 3) we will write differently: 2 + 4 / (x0 – 3) = y0;

we will solve: 4 / (x0 – 3) = y0 – 2;

x0 – 3 = 4 / (y0 – 2); hence,

x0 = 3 + 4 / (y0 – 2).

We get that when у0 = 2, the expression with the variable у0 does not make sense (you cannot divide by 0).

Answer: D (y) = (-∞; 3) ⋃ (3; + ∞), E (y) = (-∞; 2) ⋃ (2; + ∞).