What represents the opposite of the function y = 1/(x²)?

To determine the function that represents the opposite of ( y = \frac{1}{x^2} ), it's important to understand what "opposite" typically refers to in the context of functions. In this case, it relates to changing the sign of the output of the function.

The original function, ( y = \frac{1}{x^2} ), produces positive output values for all x (since ( x^2 ) is always positive for non-zero x). To find the opposite function, we would need to take the negative of the output, resulting in ( y = -\frac{1}{x^2} ).

This means that for every positive value that ( \frac{1}{x^2} ) gives, the opposite function would yield the corresponding negative value. Hence, this transformation effectively reflects the graph of the original function across the x-axis.

Therefore, ( y = -\frac{1}{x^2} ) accurately represents the opposite of the original function. This is why the correct answer is that the function representing the opposite is ( y = -\frac{1}{x^2} ).