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  • Let f : (2, ∞) and R be the function defined by f(x) = x2 – 4x + 5, then the range of f is (a) R

Let f : [2, \infty )  and R be the function defined by f(x) = x\textsuperscript{2} - 4x + 5, then the range of f is

\\(a) R\\ (b) [1, \infty ) \\(c) [4, \infty ) \\(d) [5, \infty ) \\

Answers (1)

(b)

\\Here, f(x) = x\textsuperscript{2} - 4x + 5 \\ Assume, y = x\textsuperscript{2}\ - 4x + 5 \\ or, x\textsuperscript{2}\ - 4x + 5 - y = 0 \\ or, x = [-4 \pm \sqrt \{ (-4)\textsuperscript{2}- 4(-4)(5-y) \} ]/2x = 2 \pm \sqrt (y-1)\\ \text{When x is real}, y-1 \geq 0\\ Therefore, y \geq 1\\ \text{Hence the range is}[1, \infty )\\

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