Question

The relationship between the speed of a car and its stopping distance can be modelled by the function

D= 0.0575v2, where D is the stopping distance, in metres, and v is the speed, in kilometres per hour.

a) Express the speed, v, as a function of D, in the form of y = af[k(x-d)] + c

b) Explain the meaning of the inverse function.

c) Graph each relation on separate axes. Label axes and title each graph.

d) State the domain and range for both functions. Give reasons for your selections.

e) Give evidence to confirm that the inverse function you found in part (a) is correct

Answer 1

The relationship between speed of a car v and the stopping distance D is given by,

a)

We have taken only the positive values of v as it represents the speed, which is a scalar quantity so the information of direction is not needed here.

b) If is an invertible function with domain X and range Y, then is the inverse function if

for every x in the domain X.

Basically inverse function reverses a function. If the function f applied to an input x gives a result y, then its inverse funtion will give x if operated on y.

c) The plot of D as a function of v is the following.

If we consider only the nonnegative values of v the graph will be,

Now if we represent v as a function of D the graph will be the following:

d)

The domain of D as a function of v can be the set of all Real numbers. But here if we consider only the magnitude of speed the domain should be the set of all the nonnegative real numbers, .

The range will be the set of all the nonnegative real numbers, .

The domain of v as a function of D is the set of all the nonnegative real numbers, and the range is also same.

If we take the negative values into account the inverse of the given function will not be possible.