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Question: If the domain of function \(f(x) = x^{2} - 6x + 7\)is \(( - \infty,\infty)\), then the range of func...

If the domain of function f(x)=x2−6x+7f(x) = x^{2} - 6x + 7is (−∞,∞)( - \infty,\infty), then the range of function is

A

(−∞,∞)( - \infty,\infty)

B

[−2,∞)\lbrack - 2,\infty)

C

(−2,3)( - 2,3)

D

(−∞,−2)( - \infty, - 2)

Answer

[−2,∞)\lbrack - 2,\infty)

Explanation

Solution

x2−6x+7=(x−3)2−2x^{2} - 6x + 7 = (x - 3)^{2} - 2 Obviously, minimum value is

–2 and maximum ∞\infty.