Question

For each of the functions below, 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. (a) f: R → R. f(x) = x²

Answer 1

The function f(x) = x² is not onto or one-to-one.

Step-by-step explanation:

A function is considered onto if every element in the codomain is mapped to by at least one element in the domain. A function is considered one-to-one if each element in the domain is mapped to a unique element in the codomain. Let's analyze the function f(x) = x²:

• Onto: The function f(x) = x² is not onto because not every real number has a preimage. For example, there is no real number x such that f(x) = -1.
• One-to-one: The function f(x) = x² is not one-to-one because different values of x can produce the same result. For example, f(2) = f(-2) = 4.