# Let $f:[2,\infty)\rightarrow R$ be the function defined by $f(x)=x^2-4x+5,$ then the range of f is

\begin{array}{1 1}(a)\;R & (b)\;[1,\infty)\\(c)\;[4,\infty) & (d)\;[5,\infty)\end{array}

Toolbox:
• Range of $f:[2,\infty) \to R$ is the set of values f(x) can take for $x \in domain\; f\;ie\;[2,\infty)$
$f:[2,\infty) \to R$

$f(x)=x^2-4x+5$

Let $x=2 \qquad f(x)=x^2-4(2) +5$

$=4-8+5=1$

Let $x=3 \qquad f(x)=x^3-4(3) +5$

$=9-12+5=2$

For $[2,\infty)$ the function takes values from $\{1,2,.......\infty\}$ we say that range of f is $[1, \infty)$

'B' option is correct