Răspuns:
Explicație pas cu pas:
a) x - 2 ≥ 0 ⇔ x ≥ 2 ⇔ x ∈ [2, +∞)
b) 9 - x^2 ≥ 0 ⇔ (x - 3)(x + 3) ≤ 0 ⇔ x ∈ [-3, 3]
c) (x - 3)/(x + 1) > 0
x | -1 3
x - 3 | ---------------------- 0 ++++++++++++
x + 1 | ------------ 0 ++++++++++++++++++
fracția | +++++++ / -------- 0 +++++++++++
⇒ x ∈ (-∞, -1) ∪ (3, +∞)
d) x + 2 > 0 ⇔ x > -2 ⇒ x ∈ (-2, +∞) (*)
x² - 4x > 0 & x² - 4x ≠ 1 ⇔ x(x - 4) > 0 & x² - 4x - 1 ≠ 0
x ∈ (-∞, 0) ∪ (4, +∞) & x ≠ 2 ± √5 ⇒ x ∈ (-∞, 2 - √5) ∪ (2 + √5, +∞) (**)
(*) ∩ (**) ⇒ x ∈ (-2, 2 - √5) ∪ (2 + √5, +∞)
