Answer:
[tex]f(x)^{-1}=40-\frac{x}{2500}[/tex] Quantity
Step-by-step explanation:
1) To find out the inverse function, let's geometrically do the test of the horizontal line by graphing this linear function.
f(x)=y
y=100,000-2500x.
Check the graph, the angular coefficient is -2500.
Suppose a horizontal line y=60. If y=60 touches the graph only once then this function is injective (one to one) and admits inverse function.
2) Let's algebraically do the procedures to find its inverse.
At first where is x, we change for y then we isolate y on the 1st member.
[tex]y=100,000-2500x\\x=100,000-2500y\\2500y=100,000-x\\y=\frac{100,000-x}{2500}\\y=40-\frac{x}{2500}\\f(x)^{-1}=40-\frac{x}{2500}[/tex]
In this inverse function, the variable x represents quantity . Because the inverse function the Domain of its original function is the Range of it, as the Range of f(x) is the Domain of [tex]f(x)^{-1}[/tex]
