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Question
The domain and range of real function f defined by f(x) = `sqrt(x - 1)` is given by ______.
Options
Domain = `(1, oo)`, Range = `(0, oo)`
Domain = `[1, oo)`, Range = `(0, oo)`
Domain = `[1, oo)`, Range = `[0, oo)`
Domain = `[1, oo)`, Range = `[0, oo)`
Solution
The domain and range of real function f defined by f(x) = `sqrt(x - 1)` is given by Domain = `[1, oo)`, Range = `[0, oo)`.
Explanation:
Given that: f(x) = `sqrt(x - 1)`
f(x) is defined if x – 1 ≥ 0
⇒ x ≥ 1
∴ Domain of f(x) = `[0, oo)`
Let f(x) = y = `sqrt(x - 1)`
⇒ y2 = x – 1
⇒ x = y2 + 1
If x is real then y ∈ R
∴ Range of f(x) = `[0, oo)`
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