100920 More problems on function operations

B if the fuel cost is to be kept at or below 4 cents

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b. If the fuel cost is to be kept at or below 4 cents per mile, at what speeds may the car be driven? c. Based on the meanings of the variables, which composite function makes sense, f g or g f ? Explain why your choice makes sense, and the other choice doesn’t. d. Construct a table of values and a graph of the composite function that you chose in part c . 9. Here f , g , and h stand for any functions, not necessarily the ones in previous problems. a. Draw an “input-output machine” diagram of the composite f g . b. Draw an “input-output machine” diagram of the composite ( f g ) ◦ h . c. Draw an “input-output machine” diagram of the composite f ◦ ( g h ). d. Are ( f g ) ◦ h and f ◦ ( g h ) the same as each other? Explain why or why not. Special rule for questions 10–14: Each question asks you to make up two functions f and g . Usually you can find an easy but uninteresting answer if you pick one of the functions to just be f ( x ) = x or g ( x ) = x . So, you are not allowed to use the plain x function in your answers.
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