Question

If $f:R\to R$ is a function defined as $f\left(x\right)=x^2-6x+16,$ then the range of $f$ is

• A. $[16,\infty )$
• B. $[7,\infty )$
• C. $[11,\infty )$
• D. $[9,\infty )$

Answer 1

The correct option is B $[7,\infty )$

Given $f:R\to R$ and
$f\left(x\right)=x^2-6x+16=(x-3{)}^2+7$
Since, $x\in R$ and we know that
$(x-3{)}^2\ge 0\Rightarrow (x-3{)}^2+7\ge 7$
Therefore, the range of $f\left(x\right)$ is $[7,\infty )$