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Difference between revisions of "1972 AHSME Problems/Problem 29"

(Created page with "==Problem== If <math>f(x)=\log \left(\frac{1+x}{1-x}\right)</math> for <math>-1<x<1</math>, then <math>f\left(\frac{3x+x^3}{1+3x^2}\right)</math> in terms of <math>f(x)</math>...")
 
(No difference)

Latest revision as of 12:55, 23 June 2021

Problem

If $f(x)=\log \left(\frac{1+x}{1-x}\right)$ for $-1<x<1$, then $f\left(\frac{3x+x^3}{1+3x^2}\right)$ in terms of $f(x)$ is

$\textbf{(A) }-f(x)\qquad \textbf{(B) }2f(x)\qquad \textbf{(C) }3f(x)\qquad \textbf{(D) }\left[f(x)\right]^2\qquad \\ \textbf{(E) }[f(x)]^3-f(x)$

Solution

$\fbox{C}$

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