Q109 / 180 · KCET 2020 · Mathematics
Let $f:[2, \infty) \rightarrow R$ be the function defined $f(x)=x^{2}-4 x+5$, then the ranges of $f$ is
- A$(-\infty, \infty)$
- Correct answerB$[1, \infty)$
- C$(1, \infty)$
- D$[5, \infty)$
Solution
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 $[1, \infty)$.
Hence, the correct answer is option: 'B'.