Calculus continuity

Question

What its the largest possible domain of f(x)= SQRT[(x-1)/(x+2)] And is it continuous everywhere it is defined?

Answer 1

x-1 >= 0

x >= 1

the domain is [1,2) u (2,infinity)

Answer 2

f(x) = √[(x-1)/(x+2)] f(x) is defined only when (x-1)/(x+2) ≥ 0

x - 1 = 0 when x = 1, and x + 2 = 0 when x = -2

When x < -2, x-1<0 and x+2<0. So, (x-1)/(x+2) > 0.

When -2 < x < 1, x-1<0 and x+2>0. So, (x-1)/(x+2) < 0.

When x = 1, (x-1)/(x+2) = 0.

When x>1, x-1 > 0 and x+2>0. So, (x-1)/(x+2) > 0

Domain of f = (-∞, -2) ∪ [1,∞).