Correct answer: (C) If f(x_n) converges,then x_n converges.
Explanation
Continuity on a compact interval makes f bounded,proving A by comparison with Σ1/n². The intermediate value theorem makes a continuous ±1-valued function constant,proving B. It also proves D. For C,take f≡0 and x_n alternating 0,1:images converge but inputs do not. **C**.