4) May you help with an explanation to understand the following practice problem:

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Q4-1: Monotonic transformation Consider a function f : R" -+ R. Let h be a (weakly) increasing function. (They may not be differentiable). Let g be g(x) = h(f(x)). What is the relationship between arg max f(@) and arg max g(ac). This question simply asks your understanding of the following concepts: Can you write down what arg max f (x)? . Do you know the definition of weakly increasing function? If you do, then the relationship is obvious. Make sure you can formally argue this! As exercise, explain why the following answers are wrong. 1. max f (x) = max g(x) 2. arg max f(x) = arg max g(x) 3. arg max g(x ) C arg max f(x )