Question

What is the implicit solution in the form f(x,y)c, where c is an arbitrary constant?

1) f(x,y) = c
2) f(x,y) = c + 1
3) f(x,y) = c - 1
4) f(x,y) = c²

Answer 1

The correct implicit solution in the form f(x,y) = c is found in option 1. The other options either add additional constants or change the nature of the arbitrary constant c, which is not in the general form requested.

Step-by-step explanation:

An implicit solution of a function in the form f(x,y) = c, where c is an arbitrary constant, is a relationship between x and y that isn't explicitly solved for one variable in terms of another. Among the options provided:

• Option 1, f(x,y) = c, is a general form for an implicit solution.
• Option 2, f(x,y) = c + 1, and option 3, f(x,y) = c - 1, include additional constants which alter the arbitrariness of c.
• Option 4, f(x,y) = c², suggests c is squared, which again imposes additional structure on the solution.

Therefore, the correct implicit solution in the form requested is provided by option 1, f(x,y) = c.