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Home  >>  CBSE XII  >>  Math  >>  Relations and Functions
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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}

Can you answer this question?
 
 

1 Answer

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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

 

answered Mar 5, 2013 by meena.p
 

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