Final answer:
The correct rule for the composition of a dilation of scale factor k=2 following a reflection over the line y=x is f(x) = 2x.
Step-by-step explanation:
The question involves finding a rule for the composition of a dilation with a scale factor k=2 following a reflection over the line y=x. First, consider a reflection over the line y=x, which swaps the x and y coordinates of any point on the plane, so the new coordinates become (y, x). Next, apply a dilation with a scale factor of 2 to these new coordinates, which means multiplying both by 2, so the final coordinates become (2y, 2x). If we write this as a function with input x (after the reflection and before the dilation), the output after the dilation would be 2x. Thus, the rule that represents this sequence of transformations is f(x) = 2x, which corresponds to option B).