$\begin{array}{l}f\left(x\right)=\{\begin{array}{l}xforx\ge 2\\ 5x-2forx<2\end{array}\\ Ifx=2,f\left(x\right)=x\Rightarrow f\left(2\right)=2\\ Ifx=\frac{4}{5}\\ f\left(\frac{4}{5}\right)=5\left(\frac{4}{5}\right)-2\Rightarrow 2\\ \therefore f\left(2\right)=f\left(\frac{4}{5}\right)\\ Differentelementshavesameimage\\ \therefore fisnotone-one\end{array}$

$\begin{array}{l}Ifx\ge 2thenf\left(x\right)=x\\ \therefore f\left(x\right)\ge 2\\ Ifx<2thenf\left(x\right)=5x-2\\ \therefore 5x<10\\ \Rightarrow 5x-2<10-2\\ \Rightarrow f\left(x\right)<8\\ \therefore Range=(-\infty ,8)\cup [2,\infty )=(-\infty ,\infty )=codomain\\ \therefore fisonto\end{array}$