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Q.
If a function $ f : [2, \infty)\rightarrow A $ defined by $ f(x) = x^2 - 4x +5 $ is a bijection, then $ A $ is equal to
AMUAMU 2014Relations and Functions - Part 2
Solution:
Given, function is $f(x) = x^{2} -4 x + 5$
which is defined as $f : \left[2, \infty\right) \rightarrow A$
Let $y=x^{2}-4x+5$
$\Rightarrow y=x^{2}-4x+4+1$
$\Rightarrow y-1=\left(x-2\right)^{2}$
From the curve, we see that At $x=2, f \left(2\right)=1$,
After that when we increase the value of $x$, the curve is increasing
$\therefore A=\left[1, \infty\right)$
