What is the solution?

Suppose that f : rn → rm and that a ∈ k, where k is a connected subset of rn . suppose further that for each x ∈ k there exists a δx > 0 such that f(x) = f(y) for all y ∈ bδx (x). prove that f is constant on k; that is, f(x) = f(a) for all x ∈ k

Suppose that two objects attract each other with a gravitational force of 16 units. if the distance between the two objects is double, what is the new force of attraction between the two objects?

Employer informs its employees that it will hold a substantial cash prize drawing for each work group at the end of each month in which no employee in the work group sustains a lost-time injury. tyra reports an injury that she sustained while operating a mechanical power press. tyra did not violate any employer safety rules when she sustained her injury. tyra’s injury requires her to miss work for two days. her employer cancels the cash prize drawing for that month for tyra’s work group because of tyra’s lost-time injury. did the employer misuse an incentive program to retaliate against tyra?