Question

If  \(f(x) = \frac{\log(\pi + x)}{\log(e + x) }\), then the function is:

• A. Increasing in \( [0, \infty) \)
• B. Decreasing in \( [0, \infty) \)
• C. Decreasing in \( [0, \frac{\pi}{e}] \) and increasing in \( [\frac{\pi}{e}, \infty) \)
• D. Increasing in \( [0, \pi] \) and decreasing in \( [\pi, \infty) \)

Hint:

For analyzing the increasing or decreasing nature of a function, compute \( f'(x) \) and determine where it is positive or negative.