Final answer:
The function f(x) = x² is neither injective nor surjective.
Step-by-step explanation:
The function f(x) = x² is neither injective nor surjective.
To show that f(x) is not injective (one-to-one), we need to find two distinct values of x that map to the same value of f(x). We can choose x = 2 and x = -2:
f(2) = 2² = 4 and f(-2) = (-2)² = 4,
So, f(2) = f(-2) = 4. This means that f(x) is not injective.
To show that f(x) is not surjective (onto), we need to find a value in the range of f(x) that does not have a pre-image in the domain of f(x). Let's consider the value y = -1:
If f(x) = -1, then x² = -1. However, there is no real number x that satisfies this equation, as the square of any real number is always non-negative.
Therefore, f(x) = x² is neither injective nor surjective.