Find the domain and the range of the real ...

NCERT Class XI Mathematics - Relations and Functions - Solutions

Question : 28 of 36

Marks: +1, -0

Find the domain and the range of the real function f defined by

f (x) =

\sqrt{x-1}

Solution:

Given f (x) =

\sqrt{x-1}

We know (x – 1) ≥ 0 ⇒ x ≥ 1 ⇒ x ∈ [1, ∞)

∴ Domain of f (x) is [1, ∞)

Let y = f (x) =

\sqrt{x-1}

⇒ y ≥ 0 and y =

\sqrt{x-1}

⇒ y ≥ 0 and

y^2

= x - 1

∴ Range of f (x) is [0, ∞)

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