NO, they are not inverse functions. Since f takes velocity to gas consumption, its inverse function would take gas consumption to velocity.

Here both f and g take velocity, v, to some other value. Take a look at the units of the result of both f and g. f(v) gives "liters per kilometer" while g(v) gives "kilometers per liter"- they arereciprocals.

Again, look at the units. f(v) gives "liters per kilometer" and h(v) must be in "liters per hour". Clearly to go from f(v) to h(v), you need to "multiply" by kilometers and "divide" by hours: you need to multiply by kilometers per hour. And what parameter tells you how many kilometers you go in one hour?I tried to find the value of g(80) and came out with the pretty ridiculous value of 159980km/L. I am almost certain I did this wrong, but I can't find any relevant info in my textbook. For g`(80) I know I have to use the inverse rule to find the derivative (which I know), but I can't find this until I have found the value of g(80).

b) Let h(v) be the gas consumption in L/h at velocity v. What is the relationship between h(v) and f(v)? Find h(80) and h`(80).

Okay, now I'm just lost. I don't even know where to start here.

c) How could you explain the practical meaning of the values of these function and their derivatives to a driver who knows no calculus?

I think I could get this on my own once I get help with the previous problems.