Question

If the domain of function $f\left(x\right)=x^2-6x+7$ is $(-\infty ,\infty )$, then the range of function is

• A. $(-\infty ,\infty )$
• B. $[-2,\infty )$
• C. $(-2,3)$
• D. $(-\infty ,-2)$

Answer 1

The correct option is B $[-2,\infty )$

$f\left(x\right)=x^2-6x+7,$ $xϵ(-\infty ,\infty )$

$=x^2-6x+9-2$

$=(x-3{)}^2-2$

Now, $(x-3{)}^2\ge 0$

$\Rightarrow f\left(x\right)\ge 0-2=-2$

$\Rightarrow f\left(x\right)ϵ(-2,\infty )$

$\Rightarrow$ Option (B)