Question

x²-4x+5 find domain and range

Answer 1

f(x) = x²- 4x+5

Since, given function is a polynomial which is defined everywhere.

Therefore, domain of function f(x) is set of all real numbers \((\mathbb{R}).\)

Now, f(x) = x²- 4x+5

 = x²- 4x+4+1

= (x-2)²+1

≥ 0+1 (∵ (x-2)² ≥ 0)

= 1

Hence, f(x) ≥ 1

⇒ f(x) ∈ [1, ∞)

Therefore, the range of function f(x) is [1, ∞).

Hence, domain of f(x) is \(\mathbb{R}.\)

And Range of f(x) is [1, ∞).