Find the domain and range of the following real functionsf(x) = 1 −

1.	Find the domain and range of the following real functionsf(x) = 1 − \|x − 3\|
Answer» Given, f(x) = 1 – \|x − 3\| Domain: We observe that f (x) is defined for all x ∈ R ∴ Domain of f = R Range: Now, 0 ≤ \|x − 3\| < ∞∀∈ R ⇒ −∞ < −\|x − 3\| ≤ 0 ∀ x∈ R ⇒ −∞ < −\|∀ − 3\| ≤ 1 ∀x ∈ R ⇒ −∞ < f(x) ≤ 1 ∀ x ∈ R Hence, Range of f = (−∞, 1)

Find the domain and range of the following real functionsf(x) = 1 − |x − 3|

Answer»

Given, f(x) = 1 – |x − 3|

Domain: We observe that f (x) is defined for all

x ∈ R

∴ Domain of f = R

Range: Now,

0 ≤ |x − 3| < ∞∀∈ R

⇒ −∞ < −|x − 3| ≤ 0 ∀ x∈ R

⇒ −∞ < −|∀ − 3| ≤ 1 ∀x ∈ R

⇒ −∞ < f(x) ≤ 1 ∀ x ∈ R

Hence, Range of f = (−∞, 1)