If (f:\mathbb{R}\to\mathbb{R}) and (f(x)=x^3+kx), which condition on (k) is sufficient for (f) to be one-one?

Correct answer: (k\ge0)

Step 1: For injectivity it is useful to check whether the function keeps moving in one direction. Step 2: When (k\ge0), both (x^3) and (kx) contribute an increasing effect, so different (x)-values give different outputs. Step 3: In parameter-based questions always check how the parameter changes increasing or decreasing behavior.