Question

find the domain and range of the function f(x)=√ x^2-25

Answer 1

✪ANSWER✪

• Domain is (-∞, -5]∪[5, ∞).
• Range is [0, ∞).

᯽CALCULATION᯽

The given function is

$f(x) = \sqrt{x² - 25}$

DOMAIN

Since f(x) ∈ ℝ, x² - 25 ≥ 0

⇒ x² - 5² ≥ 0

⇒ (x - 5)(x + 5) ≥ 0

⇒ x ≤ -5 or x ≥ 5

⇒ x∈ (-∞, -5]∪[5, ∞)

RANGE

We know that

x² - 25 ≥ 0

⇒ $\sqrt{x² - 25} ≥ 0$

⇒ f(x) ≥ 0

⇒ f(x)∈ [0, ∞)