Question

If a function $f:[2,\infty )\to B$ defined by$f\left(x\right)=x^2-4x+5$ is a bijection, then B is

• A. $R$
• B. $[1,\infty )$
• C. $[4,\infty )$
• D. $[5,\infty )$

Answer 1

The correct option is B $[1,\infty )$

Since, the function is bijection

Therefore, it is strictly increasing or decreasing in $[2,\infty )$

Since, $f\left(2\right)=1$ and $f\left(\infty \right)=\infty$

Therefore, it is increasing

And it range is $[1,\infty )$