Question

The demand function for an auto parts manufacturing company is given by f(x) = 100000 - 2500x , where x represents price and f(x) represents quantity. f^-1 (x) = _______. In the inverse function, the variable X represents _____

Answer 1

to solve switch x and y and solve for y. so f^-1(x)=(x-100000)/(-2500). and x will rep the quantity.

Answer 2

`f^(-1)(X)=(100000-X)/(2500)`

The variable X represents the quantity.

Explanation:

We are given that

The demand function for an auto parts manufacturing company is fiven by

f(x)=100000-25 x

Where x=Represents price

f(x)= Represents quantity

We have to find inverse function
`f^(-1)(X)`

Let f(x)=X

`X=100000-2500 x`

`2500x=100000-X`

`x=(100000-X)/(2500)`

Substituting the value of x then we get

`f^(-1)(X)=(100000-X)/(2500)`

Therefore, the inverse function

`f^(-1)(X)=(100000-X)/(2500)`

Where X= Represents the quantity

`f^(-1)(X)`=Represents price