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Question
The domain and range of the function f given by f(x) = 2 – |x – 5| is ______.
Options
Domain = R+, Range = `(– oo, 1]`
Domain = R, Range = `(– oo, 2]`
Domain = R, Range = `(– oo, 2)`
Domain = R+, Range = `(– oo, 2]`
Solution
The domain and range of the function f given by f(x) = 2 – |x – 5| is Domain = R, Range = `(– oo, 2]`.
Explanation:
Given that: f(x) = 2 – |x – 5|
Here, f(x) is defined for x ∈ R
∴ Domain of f(x) = R
Now, x – 5 ≥ 0
⇒ – |x – 5| ≤ 0
⇒ 2 – |x – 5| ≤ 2
⇒ f(x) ≤ 2
∴ Range of f(x) = `(-oo, 2]`
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