Question

If $f:[1,\infty )\to B$ defined by the function $f\left(x\right)=x^2-2x+6$ is a surjection, then $B$ is equal to

• A. $[1,\infty )$
• B. $[5,\infty )$
• C. $[6,\infty )$
• D. $[2,\infty )$

Answer 1

The correct option is B $[5,\infty )$

$f\left(x\right)=x^2-2x+6$
$f\left(x\right)=(x-1{)}^2+5$
$f\left(x\right)$ will have its vertex at $(1,5)$
$\therefore$ Range of $f\left(x\right)$ in domain $[1,\infty )$is $[5,\infty )$
$\therefore B=[5,\infty )$