Question

As \( x \) is increased from \( -\infty \) to \( \infty \), the function \( f(x) = \frac{e^x}{1+e^x} \) behaves as

• A. Monotonically increases
• B. Increases to a maximum value and then decreases
• C. Monotonically decreases
• D. Decreases to a minimum value and then increases

Hint:

The sigmoid function is a common example of a monotonically increasing function.

Answer 1

The Correct Option is A

The given function \( f(x) = \frac{e^x}{1+e^x} \) is a sigmoid function. As \( x \) increases from \( -\infty \) to \( \infty \), the value of \( f(x) \) starts from 0 (as \( x \to -\infty \)) and increases monotonically toward 1 (as \( x \to \infty \)). Therefore, the function monotonically increases. Hence, the correct answer is option (1).