I have utility function given by:
$U(x_1, x_2) = \begin{cases} x_1+x_2 & \text{if $x_1+x_2<6$} \\ 6 & \text{if $6\leq x_1+x_2\leq10$} \\ x_1 + x_2 & \text{if $x_1+x_2>10$} \end{cases}$
If I transform this to this:
$F(U(x_1, x_2)) = \begin{cases} U(x_1, x_2)+4 & \text{if $U(x_1, x_2)<6$} \\ 10 & \text{if $U(x_1, x_2)=6$} \\ U(x_1, x_2) & \text{if $U(x_1, x_2)>10$} \end{cases}$
Is it strictly increasing function transformation?
Thanks guys