Question

The domain and range of real function f defined by f(x) = `sqrt(x - 1)` is given by ______.

Options

• Domain = `(1, oo)`, Range = `(0, oo)`

• Domain = `[1, oo)`, Range = `(0, oo)`

• Domain = `[1, oo)`, Range = `[0, oo)`

• Domain = `[1, oo)`, Range = `[0, oo)`

Answer 1

The domain and range of real function f defined by f(x) = `sqrt(x - 1)` is given by Domain = `[1, oo)`, Range = `[0, oo)`.

Explanation:

Given that: f(x) = `sqrt(x - 1)`

f(x) is defined if x – 1 ≥ 0

⇒ x ≥ 1

∴ Domain of f(x) = `[0, oo)`

Let f(x) = y = `sqrt(x - 1)`

⇒ y² = x – 1

⇒ x = y² + 1

If x is real then y ∈ R

∴ Range of f(x) = `[0, oo)`