Question

MT&A uses the function, f(x) = 475 - 15x, to depreciate smartphones, where f represents the value of a smartphone and x represents the number of months since its purchase.

Find f⁻1, and explain what it represents in this situation.

a) f⁻1(x) = (475 - x) / 15

b) f⁻1(x) = 475 / x - 15

c) f⁻1(x) = 475 / 15 - x

d) f⁻1(x) = (x - 475) / 15

Answer 1

The inverse function f⁻¹(x) = (x - 475) / 15 represents the number of months since the purchase of the smartphone based on its current value. This relationship is obtained by solving y = 475 - 15x for x to find the inverse.

Step-by-step explanation:

MT&A depreciates smartphones using the function f(x) = 475 - 15x, where f represents the value of a smartphone, and x represents the number of months since its purchase. To find the inverse f⁻¹(x), we follow several steps. First, we replace f(x) with y: y = 475 - 15x. To find f⁻¹, we swap x and y and then solve for the new y. Doing this gives us x = 475 - 15y, which when solved for y gives y = (x - 475) / 15. Therefore, the correct inverse function is f⁻¹(x) = (x - 475) / 15, which represents option d). The inverse function represents the number of months that have passed since the purchase of the smartphone based on its current value.