Question

pleaseee help meeee For questions 9 - 10, answer the question about inverses. 9. The function m(d) below relates the miles Bob can drive his rental car and the numbers of dollars it will cost. 10. The function a(h) below relates the area of a triangle with a given base 7 and the height of the triangle. It takes as input the number of dollars spent and returns as output the number of miles. It takes as input the height of the triangle and returns as output the of the triangle. m(d) = 40(d- 35) ain= Write the equation that represents the inverse function, d(m), which takes the number of miles driven, m, as input and returns the number of dollars owed, d. Write the equation that represents inverse function, h(a), which takes triangle's area as input and returns height of the triangle.

Answer 1

First problem:

Find the inverse of the function

m = 40 (d - 35)

Recall that for the inverse function we need to solve for d in terms of m (reverse the dependence), so we proceed to isolate d on the right hand side of the equation:

divide both sides by 40

m/40 = d - 35

now add 35 to both sides:

m/40 + 35 = d

The inverse function (dollars in terms of miles) is given then by:

d(m) = 1/40 m + 35

Second problem:

a = 7 * h / 2

in order to find the inverse function (as h in terms of a) we solve for h on the right hand side of the equation as shown below:

multiply both sides by 2:

2 * a = 7 * h

now divide both sides by 7 in order to isolate h on the right

2 a / 7 = h

So our inverse function of height in terms of area is given by:

h(a) = (2 a) / 7