The function \(f(x) = 2x + 3\) is defined for \(x \leq 0\). To find the inverse, solve \(y = 2x + 3\) for \(x\):

\(y - 3 = 2x\)

\(x = \frac{y - 3}{2}\)

Thus, \(f^{-1}(x) = \frac{x - 3}{2}\).

The graphs of \(y = f(x)\) and \(y = f^{-1}(x)\) are reflections of each other in the line \(y = x\).

To find the intersection, set \(f(x) = f^{-1}(x)\):

\(2x + 3 = \frac{x - 3}{2}\)

Multiply through by 2 to clear the fraction:

\(4x + 6 = x - 3\)

\(3x = -9\)

\(x = -3\)

Substitute \(x = -3\) back into \(f(x)\):

\(y = 2(-3) + 3 = -3\)

Thus, the point of intersection is \((-3, -3)\).