Find the domain and range of the function f(x) =

Maths Functions, Limits, Continuity and Differentiability General Subjective Type

Published on: August 12, 2026

Find the domain and range of the function

f(x) =

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Sol.  – 1 ≤ cos 3x ≤ 1 ∀ x ∈ R

⇒ – 1 ≤ –cos 3x ≤ 1 ∀ x ∈ R

⇒ 1 ≤ 2 – cos 3x ≤ 3 ∀ x ∈ R

∴ Domain of f is 'R'.

For range ;

Let f(x) = y

∴ y =

⇒ = 2 –cos 3x

⇒ cos 3x = 2 –

⇒ –1 ≤ 2 – ≤ 1

⇒ –3 ≤ – ≤ 1

⇒ 3 ≥ ≥ 1

⇒ ≤ y ≤ 1

∴ Range of f is [1/3, 1]

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