Question

If \( e^x = y + \sqrt{1 + y^2} \), then the value of y is:

• A. \( \frac{1}{2}(e^x - e^{-x}) \)
• B. \( \frac{1}{2}(e^x + e^{-x}) \)
• C. \( e^x - e^{-x} \)
• D. \( e^x + e^{-x} \)

Hint:

Exponential equations can often be solved by isolating the desired variable and using properties of exponents.

Answer 1

The Correct Option is B

Step 1: Solve for y. The given equation can be rearranged and solved for \( y \) as: \[ y = \frac{1}{2}(e^x + e^{-x}) \]
Step 2: Conclusion. Thus, the value of \( y \) is \( \frac{1}{2}(e^x + e^{-x}) \).