Let f : [2, ∞) → R be the function defined by f (x) = x²–4x+5, then the range of f is

Question

Let f : [2, ∞) → R be the function defined by f (x) = x 2 –4x+5, then the range of f is

Philoid · Accepted Answer

Given that, f (x) = x²–4x+5

Let f(x) = y

⇒ y = x²–4x+5

⇒ y = x²–4x+4+1

⇒ y = (x-2)²+1

⇒ y-1 = (x-2)²

⇒ (x-2)²= y-1

⇒

Now, if f is real valued function then

⇒ y-1 ≥ 0

⇒ y ≥ 1

∴ the range of f is [1, ∞).

Let f : [2, ∞) → R be the function defined by f (x) = x2–4x+5, then the range of f is