Question

A real estate company balances the books for its business on the first day of each month. It hopes to sell houses every other day of the month. The average number of houses, S, the company sells each day, t, is represented by the inverse of the function Inverse of S is equal to the quantity t squared plus 4 times t minus 12 end quantity over the quantity t squared minus 9 times t plus 14 end quantity

Which equation represents the average sales each day for the real estate company?

Answer 1

To find the equation that represents the average sales each day, we need to first find the inverse of the function and then solve for S.

Inverse of S is given by:

t = (S^2 + 4S - 12)/(S - 7)(S - 2)

We can rewrite this as:

t(S - 7)(S - 2) = S^2 + 4S - 12

Expanding the left side:

t(S^2 - 9S + 14S - 14) = S^2 + 4S - 12

Simplifying:

tS^2 - 9tS + 14tS - 14t = S^2 + 4S - 12

Rearranging:

(t - 1)S^2 + (5t - 4)S - 12t + 12 = 0

Finally, solving for S:

S = [(4 - 5t) ± sqrt((5t - 4)^2 + 4(t - 1)(12t - 12))] / 2(t - 1)

Therefore, the equation that represents the average sales each day for the real estate company is:

S = [(4 - 5t) ± sqrt((5t - 4)^2 + 4(t - 1)(12t - 12))] / 2(t - 1)