Question

Indicate whether the function is onto, one-to-one, neither or both. if the function is not onto or not one-to-one, give an example showing why. f: R → R. f(x) = x²

Answer 1

The function f(x) = x² is neither onto nor one-to-one.

Step-by-step explanation:

The function f: R → R given by f(x) = x² is neither onto nor one-to-one.

To determine if the function is onto, we need to see if every element in the range of the function is mapped to by at least one element in the domain.

Since the function only produces positive values, it does not map to any negative numbers in the range. Therefore, it is not onto.

To check if the function is one-to-one, we need to see if different elements in the domain are mapped to different elements in the range. However, since both positive and negative values of x² yield positive values in the range, the function is not one-to-one.

An example where the function is not one-to-one would be f(2) = f(-2) = 4, where different elements in the domain are mapped to the same element in the range.