Function R→R defined as choose the correct statement.

Solution: Analyze injectivity and surjectivity for f(x) = x^2 + 2x.

Rewrite the function by completing the square: f(x) = x^2 + 2x = (x+1)^2 - 1.

• Not one-to-one (injectivity fails): a quadratic symmetric about its vertex gives the same value for two different x. For example, f(0) = 0 and f(-2) = 0, so distinct inputs map to the same output.

• Not onto R (surjectivity onto the real numbers fails): since f(x) = (x+1)^2 - 1, the smallest possible value is -1, so the range is [-1, ∞) and no real x produces y < -1.

Conclusion: The function is neither one-to-one nor onto R, so none of the given properties (being bijection, surjection onto R, or one-one on R) hold.