Question

Find the domain and range of f(x) =√x^2 − 3

Answer 1

EXPLANATION :

$\sf \: f(x) = { \sqrt{x} }^{2} - 3$

$\implies \sf \: f(x) = x - 3$

For all natural value of x ,f(x) is natural number

$\sf \: domain : N \to \: N$

$\sf \: range : N \to \: N$

Answer 2

Answer:

Step-by-step explanation:

1). Let assume the task is: to find the range and domain of f(x) = $(\sqrt{x})^2 - 3$

Domain (D) is set of all positive real numbers and zero.

D = { x : x ≥ 0 } or x ∈ [ 0, ∞ )

Range (R) is: $f_{min}$(0) = 0 - 3 = - 3 ⇒ R = { y: y ≥ - 3 } or y ∈ [- 3, ∞ )

Attachment 1.

2). Now, if task is to find domain and range of $f(x)=\sqrt{x^2} -3$ , then

Domain (D) is all real numbers, x ∈ ( - ∞ , ∞ )

Range (R) is y ≥ - 3, or y ∈ [ - 3 , ∞ )

Attachment 2.