Question

Find the equation representing the inverse function D(m), relating the number of miles driven as input and the number of dollars owed as output, given the function M(d):

a) D(m) = 35(40 - d)
b) D(m) = 40(d - 35)
c) D(m) = 35(d - 40)
d) D(m) = 40(35 - d)

Answer 1

The equation representing the inverse function D(m) is D(m) = 35(d - 40). To find the inverse function, we solve for d in terms of m by rearranging the given function M(d) and substituting D(m) for M(m).

Step-by-step explanation:

The equation representing the inverse function D(m) is c) D(m) = 35(d - 40).

To find the inverse function, we need to solve for d in terms of m. Let's start with the given function M(d):

M(d) = 40(d - 35)

Now, we can solve for d by rearranging the equation:

d = (M(d) + 35) / 40

Next, we replace d with m and rewrite the equation:

m = (M(m) + 35) / 40

Simplifying the equation further gives:

M(m) = 40(m - 35)

Finally, we substitute D(m) for M(m) to represent the inverse function:

D(m) = 35(d - 40)

The representation of the inverse function D(m) as D(m) = 35(d - 40) is derived through the substitution of D(m) for M(m) in the simplified equation M(m) = 40(m - 35).