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Algebra Level 4

If f ( x ) = ln ⁡ ( 1 + x 1 − x ) f(x)=\ln \left (\dfrac{1+x}{1-x} \right ) then which of these answer choices is true?

For more questions on logarithms try this set Logs of logs .
f ( x 1 ) ⋅ f ( x 2 ) = f ( x 1 + x 2 ) f(x_1)\cdot f(x_2)=f(x_1+x_2) f ( x + 1 ) + f ( x ) = f ( x 2 + x ) f(x+1)+f(x)=f(x^2+x) f ( x + 2 ) − 2 f ( x + 1 ) + f ( x ) = 0 f(x+2)-2f(x+1)+f(x)=0 f ( x 1 ) + f ( x 2 ) = f ( x 1 + x 2 1 + x 1 x 2 ) f(x_1)+f(x_2)=f \left (\frac{x_1+x_2}{1+x_1x_2} \right )

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Gautam Sharma by Gautam Sharma , 23, India

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1 solution

Alex Li
May 5, 2015

Just substitute x = 1 x=1 to get f ( 1 ) = ∞ f(1)=\infty , and there is only one answer choice that fits this criteria.

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