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1963 AMC 12 Question 30

AMC12 · 1963 AMC 12

Question 30

Let

$$
F=\log\frac{1+x}{1-x}.
$$

Form a new function $G$ by replacing each $x$ in $F$ by

$$
\frac{3x+x^3}{1+3x^2},
$$

and simplify. The simplified expression $G$ is equal to:
  1. $-F$
  2. $F$
  3. $3F$
  4. $F^3$
  5. $F^3-F$