Domain Restriction for Inverse

No, because the function is not one-one (injective) on \(\mathbb{R}\)

Explanation

For a function to have an inverse, it must be bijective (one-one and onto). The function \( f(x) = x^2 \) fails the horizontal line test on \( \mathbb{R} \) because distinct inputs (e.g., \( x=2 \) and \( x=-2 \)) map to the same output (\( 4 \)). Therefore, it is not injective and does not have an inverse unless the domain is restricted (e.g., to \( x \ge 0 \)).