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 equals to

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

Answer 1

Answer: (B)

$[5,\infty )$

$f\left(x\right)=x^2-2x+6$ is a surjection.
So the range of $f\left(x\right)$ will be equal to its codomain.
$f\left(x\right)=x^2-2x+6$
$f^1\left(x\right)=2x-2$
$=2(x-1)$
$f\left(x\right)$ will be increasing when $x⩾1$.
$\therefore f\left(1\right)=1-2+6$
$=5$
$\therefore B=[5,\infty )$