Question

Let $f:[\alpha ,\infty )\to [x,\infty ),f\left(x\right)=x^2-6x+5$ then find three possible value of ${}^{\prime }{\alpha }^{\prime }$ if $f\left(x\right)$ is onto.

Answer 1

$f\left(x\right)=x^2-6x+5$

By graph we can say $xϵ[3,\infty )$ then,

$f\left(x\right)ϵ[-4,\infty )$

when $xϵ[5,\infty )$ then $f\left(x\right)ϵ[0,\infty )$

$\therefore$ Possible value of $\alpha$ only $3\&5$