Hey I’m facing some trouble understanding the question here, the question states that f(x) is a positive real function and g(x) = log f(x). Just want some clarification over:

- What is a positive real function?
- I chose the answer “If x_{max} is a point where f(x_{max}) is a local minimum, then g(x_{max}) is also a local
**minimum**” assuming that the answer is correct since the derivative of log would be \frac{1}{x}, but this was wrong. - The question feedback did suggest that the answer in (2) would be true if we compose f with a decreasing function, but log isn’t? I do understand the terms compose, decreasing, but I just don’t understand this sentence as a whole.

Appreciate the help if anyone could shed some light over this

Thanks!