If the payoff variable is non-negative, you can use square root for risk aversion and square for risk seeking. If the payoff can be negative, then you first have to add a constant to make it non negative.
Could you please tell me about other utility functions? I'm going to learn more about it(specially for risk aversion)? If there are some reference about utility functions like : log , ln , square root , square functions and ... let me know ..