Find All the Real-Number Roots of the Equation $e ^ { x } - e ^ { - x } = 1$

question 11

Multiple Choice

Find all the real-number roots of the equation. Give an exact expression for the root and also(where appropriate) a calculator approximation rounded to three decimal places. $e ^ { x } - e ^ { - x } = 1$

• A) \(x = \pm \ln \frac { - 1 + \sqrt { 5 } } { 2 } \approx \pm 0.479\)
• B) \(x = \ln \frac { 1 + \sqrt { 5 } } { 2 } \approx 0.481\)
• C) \(x = \ln ( 1 + \sqrt { 5 } ) \approx 0.623\)
• D) \(x = \ln \frac { 1 + \sqrt { 5 } } { 2 } \approx 0.481 ; \ln \frac { 1 - \sqrt { 5 } } { 2 } \approx 0.479\)
• E) no solution

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