Find the Domain of a Function y = arcsin x + 3/4

Find the domain of the function y = arcsin (x + 3/4).
Since, y = arcsin x belongs to [- 1; 1], then:
– 1 <= x + 3/4 <= 1;
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:
– 1 – 3/4 <= x <= 1 – 3/4;
(- 4 * 1 – 3 * 1) / 4 <= x <= (4 * 1 – 3 * 1) / 4;
(- 4 – 3) / 4 <= x <= (4 – 3) / 4;
– 7/4 <= x <= 1/4;
– 1.75 <= x <= 1.25;
Answer: – 1.75 <= x <= 1.25.