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in Sets, Relations and Functions by (25.7k points)
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Find the domain and range of the following real functions

f(x) = 1 − |x − 3|

1 Answer

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Best 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)

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