Given f(x) = ((1+x)/(1-x)).

May 25, 2026Mathematics

ScanSolve AI Answer

May 25, 2026

Answer

-f(x)$.

Hey Adora — ready when you are.

Step 1: Show that $f(x)$ is an odd function. A function $f(x)$ is odd if $f(-x) = -f(x)$ . Given $f(x) = \ln\left(\frac{1+x}{1-x}\right)$ . Substitute $-x$ into the function: $f(-x) = \ln\left(\frac{1+(-x)}{1-(-x)}\right) = \ln\left(\frac{1-x}{1+x}\right)$ Using the logarithm property $\ln\left(\frac{a}{b}\right) = -\ln\left(\frac{b}{a}\right)$ :

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Hey Adora — ready when you are. Step 1: Show that f(x) is an odd function.

Asked on May 25, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on May 25, 2026

Hey Adora — ready when you are. Step 1: Show that f(x) is an odd function. A function f(x) is odd if f(-x) = -f(x). Given f(x) = ((1+x)/(1-x)). Substitute -x into the function: f(-x) = ((1+(-x))/(1-(-x))) = ((1-x)/(1+x)) Using the logarithm property ((a)/(b)) = -((b)/(a)): f(-x)