Let f: [2, ∞) → R be a function defined by f(x) = x2 - 4x + 5. The ra…

Given that, f(x) = x² - 4x + 5

Let (f(x)) = y

$y = x^2-4x+5⇒y=x^2-4x+4+1$

$y=(x-2)^2+1$

$y-1=(x-2)^2⇒(x-2)^2=y-1$

$x-2=\sqrt{y-1}⇒x=2+\sqrt{y-1}$

Now, if f is real valued function then.

$⇒ y-1≥0$

$⇒ y≥1$

The range of f is [1, ∞).