if f(x) = -x² + 6x - 8 is a bijection , then find the domain and range

Dear Student,
Please find the solution to the asked query:
The graph of the function after putting few values of x will be :

Here we can see that for two values of x we have same y so it is not bijection, however its range can be found out.
$$\begin{gathered} \mathrm{f}\left(\mathrm{x}\right)= -\left({\mathrm{x}}^2-6\mathrm{x}+8\right) \\ =-\left({\mathrm{x}}^2-6\mathrm{x}+9-9+8\right) \\ =1-{\left(\mathrm{x}-3\right)}^2 \\ \mathrm{So} \mathrm{maximum} \mathrm{value} \mathrm{is} 1 \mathrm{at} \mathrm{x} = 3 \mathrm{and} \mathrm{minimum} \mathrm{value} \mathrm{is} -\infty . \\ \mathrm{Also} \mathrm{you} \mathrm{can} \mathrm{put} \mathrm{any} \mathrm{values} \mathrm{of} \mathrm{x} \mathrm{so} \mathrm{domain} \mathrm{is} \mathrm{x}\in \mathrm{R} \mathrm{and} \\ \mathrm{range} \mathrm{is} \mathrm{x}\in (-\infty ,1] \end{gathered}$$