# Strictly increasing function transformation

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

• Are you sure your definition makes sense? If I were you, I would first F alone, without reference to U. – Arthur Oct 16 '19 at 23:14
• @Arthur Why would that be helpful? Even from this formulation, one can see the problem. – Giskard Oct 17 '19 at 6:32
• Thanks, guys, I got it later its a non-decreasing function but not a strictly increasing one. @Arthur I wrote the function like that because it is more apparent rather than writing it without referring to U, anyways thanks for trying – CheeseBurger Oct 17 '19 at 19:57