The solution is bit dependent on what the for loop means in this context . Whether the for loop runs for N times or N-1 times defines the solution.
If for loop runs for N-1 times :
For loop runs for f(x) - 1 times and while loop runs for f(x) times . Hence the only way these programs can be equivalent if none of the programs run i.e if f(x) < 1
If for loop runs for N times :
it's always identical