Question

If the domain of the 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

Answer: (B)

$[-2,\infty )$

Now, $x^2-6x+7={(x-3)}^2-2$

Since, $(x-3{)}^2$ will always be positive or zero. So minimum value it can attain is $0$.

So the minimum value of f(x) will be $-2$ and maximum value will be $\infty$