Given the function \(f: \mathbb{R} \rightarrow \mathbb{R}\) defined as \(f(x) = x^2\), determine if this function is surjective (onto).

Step 1 ：Step 1: A function \(f: A \rightarrow B\) is said to be surjective (onto) if for every \(b \in B\), there exists an \(a \in A\) such that \(f(a) = b\).

Step 2 ：Step 2: In our case, \(A = B = \mathbb{R}\), the set of all real numbers, and \(f(x) = x^2\).

Step 3 ：Step 3: For the function to be surjective, every real number should be the square of some real number. But we know that the square of any real number is always non-negative, i.e., \(x^2 \geq 0\) for all \(x \in \mathbb{R}\).

Step 4 ：Step 4: Therefore, for any real number \(b < 0\), there is no real number \(a\) such that \(a^2 = b\). This means that the function \(f(x) = x^2\) is not surjective.