Match List I with List II

List I List II
A. \(f(x) = \frac{x}{{1 + {x^2}}}\) I. Rf = (1, ∞)
B. \(f(x) = \frac{3}{{2 - {x^2}}}\) II. Rf = (-∞, 0) ∪ \(\left[ {\frac{3}{2},\infty } \right]\)
C. \(f(x) = \frac{1}{{\sqrt {x - \left[ x \right]} }}\) III. \({R_f} = \left[ { - \frac{1}{2},\frac{1}{2}} \right]\)
D. \(f\left( x \right) = \frac{1}{{2 - \sin 3x}}\) IV. \({R_f} = \left[ {\frac{1}{3},1} \right]\)

Choose the correct answer from the options given below:

1
A - III, B - I, C - II, D - IV
2
A - III, B - II, C - I, D - IV
3
A  - II, B - IV, C - I, D - III
4
A - II, B - I, C - IV, D - III 

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