You are asked to design the given problem using genetic algorithm. Explain your design approach in terms of following: Vague answered will be penalized. Calculator can be utilized.

"Find the value of x where x - (1/x) will be maximum in the range of [0, 16]"

a. Design the Problem Solving Agent formulation & fitness function

b. Describe the Chromose/String representation of a state constituting a parent

c. Detail the approach toward the selection, crossover and mutation steps for this problem. Show this with only one iteration of numerical example and the selection step alone for second iteration.

d. Explain the significance of "mutation" in the genetic algorithm with given example.