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Question
Let f: `[2, oo)` → R be the function defined by f(x) = x2 – 4x + 5, then the range of f is ______.
Options
R
`[1, oo)`
`[4, oo)`
`[5, oo)`
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Solution
Let f: `[2, oo)` → R be the function defined by f(x) = x2 – 4x + 5, then the range of f is `[1, oo)`.
Explanation:
We have f(x) = x2 – 4x + 5
= (x2 – 4x + 4) + 1
= (x – 2)2 + 1
Now (x – 2)2 ≥ 0, ∀ x ∈ `[2, oo)`
⇒ (x – 2)2 + 1 ≥ 1
⇒ f(x) ≥ 1
Hence, range is `[1, oo)`.
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