Question

The range of the function $f(x)=x^2-6x+7$ is :

• A. $(-\infty ,0)$
• B. $[-2,\infty )$
• C. $(-\infty ,\infty )$
• D. $(-\infty ,-2)$

Answer 1

Answer: (B)

Let $y=f(x)=x^2-6x+7$
$y=x^2-6x+9+7-9$
$=(x-3{)}^2-2$
$\Rightarrow$ Minimum value is $-2$ and maximum value is $\infty$.
$\therefore$ Required range is $[-2,\infty )$