The function $$f: \mathbb{R} \rightarrow \mathbb{R}$$, $$f(x) = \frac{x^2 + 2x - 15}{x^2 - 4x + 9}$$, $$x \in \mathbb{R}$$ is

$$f(x) = \frac{x^2+2x-15}{x^2-4x+9}$$. Denominator: discriminant = 16-36 = -20 < 0, always positive.

Check one-one: f(3) = (9+6-15)/(9-12+9) = 0/6 = 0. f(-5) = (25-10-15)/(25+20+9) = 0/54 = 0. Not one-one.

Check onto: Let y = f(x). Then x²+2x-15 = y(x²-4x+9). (1-y)x² + (2+4y)x - (15+9y) = 0.

For real x: D ≥ 0. (2+4y)² + 4(1-y)(15+9y) ≥ 0.

4+16y+16y² + 4(15+9y-15y-9y²) ≥ 0. 4+16y+16y²+60-24y-36y² ≥ 0. -20y²-8y+64 ≥ 0. 20y²+8y-64 ≤ 0.

5y²+2y-16 ≤ 0. Roots: y = (-2±√(4+320))/10 = (-2±18)/10. y ∈ [-2, 8/5].

Range is [-2, 8/5] ≠ ℝ. Not onto.

The correct answer is Option (4): neither one-one nor onto.