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Let $f:[2, \infty) \rightarrow R$ be the function defined $f(x)=x^{2}-4 x+5$, then the ranges of $f$ is
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Verified Answer
The correct answer is:
$[1, \infty)$
We have,
$\begin{aligned}
&f(x)=x^{2}-4 x+5 \\
&f(x)=x^{2}-4 x+4+1 \\
&f(x)=(x-2)^{2}+1
\end{aligned}$
$\therefore$ Range of $f(x)$ is $[1, \infty)$.
$\begin{aligned}
&f(x)=x^{2}-4 x+5 \\
&f(x)=x^{2}-4 x+4+1 \\
&f(x)=(x-2)^{2}+1
\end{aligned}$
$\therefore$ Range of $f(x)$ is $[1, \infty)$.
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