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A function $\mathrm{f}: \mathrm{A} \rightarrow \mathrm{R}$ is defined by the equation $\mathrm{f}(\mathrm{x})=\mathrm{x}^{2}-4 \mathrm{x}+5$
where $\mathrm{A}=(1,4)$. What is the range of the function?
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where $\mathrm{A}=(1,4)$. What is the range of the function?
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The correct answer is:
$[1,5)$
$\begin{aligned} f(x) &=x^{2}-4 x+5=(x-2)^{2}+1 \\ f(1) &=2, f(4)=5 \end{aligned}$
$\therefore$ Range $f(x)=[1,5)$
$\therefore$ Range $f(x)=[1,5)$
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