Let f: [2, oo) → R be the function defined by f(x) = x2 – 4x + 5, then the range of f is ______.

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Let f: [2, oo) $\to$ 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 $\geq$ 0, ∀ x ∈ [2, oo) $\Rightarrow$ (x – 2)2 + 1 $\geq$ 1 $\Rightarrow$ f(x) $\geq$ 1 Hence, range is [1, oo).

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