_ (a) Explain the meaning of Dog 500. (b) Use your explanation from part (a) to approximate 10g2 500 without using a calculator. Explain your method. ((5) w describe the relationship between the func- tions ' - fa) = 2. and 90\") = 10g2 35" Frame your response in the context of what we have learned in this class. In particular, be sure to include the following: I. The meaning of the function g and how this relates to the function f. Include at least 5 specic examples of evaluating the function g at specic inputs of your choice to help with your explanation. 2. The relationships between the domains and ranges of the two functions and the reason for these relationships. 3. The relationship between the graphs of the functions and the reason for this relationship. Include hand-drawn copies of these graphs to help with your explanation. 4. Observations about the compositions g(f(x)) and f(g(x)). In particu- lar, you should simplify each composition and explain why the compositions simplify as they do. 5. The meanings of the expressions 10g2(25'4) and 21035214, Use these meanings to simplify each expression. Explain your reasoning thoroughly