Domain of √x^-1+1/√x^-3x+2

Question

Domain of √x²-1+1/√x²-3x+2

Answer 1

√(x²-1) + 1/(√(x²-3x+2))  = √((x-1)(x+1)) + 1/(√((x-2)(x-1))

 

Domain:  {x l (x-1)(x+1) ≥ 0 and (x-2)(x-1) > 0}

 

When x ≤ -1, (x-1)(x+1) ≥ 0

When -1 < x < 1, (x-1)(x+1) < 0

When x≥1, (x-1)(x+1) ≥ 0

 

So, (x-1)(x+1)≥0 on (-∞, -1] ∪ [1,∞)

 

 

When x < 1, (x-1)(x-2) > 0

When 1≤x≤2, (x-1)(x-2) ≤ 0

When x > 2, (x-1)(x-2) > 0

 

So, (x-1)(x-2) > 0 on (-∞, 1)  ∪ (2,∞)

 

Domain: (-∞, -1] ∪ (2, ∞)