Find the domain and range of each of the following real valued functio

1.	Find the domain and range of each of the following real valued functions : f(x) = √(x-1)
Answer» f(x) = √(x-1) We know, The square of a real number is never negative. Clearly, f(x) takes real values only When x – 1 ≥ 0 ⇒ x ≥ 1 ∴ x ∈ [1, ∞) Thus, Domain of f = [1, ∞) When x ≥ 1, We have, x – 1 ≥ 0 Hence, \(\sqrt{x-1}\) ≥ 0 ⇒ f(x) ≥ 0 ∴ f(x) ∈ [0, ∞) Thus, Range of f = [0, ∞)

Find the domain and range of each of the following real valued functions : f(x) = √(x-1)

Answer»

f(x) = √(x-1)

We know,

The square of a real number is never negative.

Clearly,

f(x) takes real values only

When x – 1 ≥ 0

⇒ x ≥ 1

∴ x ∈ [1, ∞)

Thus,

Domain of f = [1, ∞)

When x ≥ 1,

We have,

x – 1 ≥ 0

Hence,

\(\sqrt{x-1}\) ≥ 0

⇒ f(x) ≥ 0

∴ f(x) ∈ [0, ∞)

Thus,

Range of f = [0, ∞)