(i) Domain : R, Range : ≤ y ≤ 1

(ii) Domain : N ∪ {0}, Range : (n! : n = 0, 1, 2,...}

(iii) Domain R – {3}, Range : R – {6}

(iv) Domain : R, Range : {1}

Sol. (i) f(x) =

Domain 4 + 3 sin x > 0 ⇒ sin x > – Always true ⇒ x ∈ R

Range – 3 ≤ 3 sin x ≤ 3

⇒ 1 ≤ 4 + 3 sin x ≥ 7 ⇒ 1 ≥ ≥ ⇒ 1 ≥ ≥ ⇒ y ∈

(ii) f(x) = x !

Domain x ∈ W ⇒ x ∈ N ∪ {0}

Range {y : y ∈ n!, where n = 0, 1, 2, 3, ......}

(iii) f(x) = = = (x + 3)

Domain x ∈ R – {3}

Range y ∈ R – {6}

(iv) f(x) = sin 2 (x 3 ) + cos 2 (x 3 )

f(x) = 1

Domain x ∈ R

Range y ∈ {1}

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