Find the Domain of a Function y = lg (x ^ 2-16) + x-3 / x ^ 2-25

Find the domain of the function y = lg (x ^ 2 – 16) + (x – 3) / (x ^ 2 – 25).

{x ^ 2 – 16> 0;

x ^ 2 – 25 ≠ 0;

{(x – 4) * (x + 4)> 0;

(x – 5) * (x + 5) ≠ 0;

{(x – 4) * (x + 4) = 0;

(x – 5) * (x + 5) ≠ 0;

{x – 4 = 0;

x + 4 = 0;

x – 5 ≠ 0;

x + 5 ≠ 0;

We transfer the known values to one side, and the unknown ones to the other side. When transferring values, their signs are changed to the opposite sign. That is, we get:

{x = 4;

x = – 4;

x ≠ 5;

x ≠ – 5;

Hence, x <- 4, x> 4, x ≠ 5, x ≠ – 5;

Answer: x <- 4, x> 4, x ≠ 5, x ≠ – 5.