Question

Carmen is writing an article for a magazine. She will be paid a fee and also will be paid for each word that is published. The total amount she can expect to be paidin dollars, can be estimated using the function f(x) = 2.5x + 150 , where is the number of words published . What is the inverse of this function?

Answer 1

The inverse function of f(x)=2.5*x+150 is f⁻¹(x)=
`(2)/(5)x-60`

Explanation:

An inverse or reciprocal function of f (x) is called another function f ⁻¹(x) that fulfills that:

If f(a)=b then f⁻¹(b)=a

That is, inverse functions are functions that do the "opposite" of each other. For example, if the function f (x) converts a to b, then the inverse must convert b to a.

To construct or calculate the inverse function of any function, you must follow the steps below:

Since f (x) or y is a function that depends on x, the variable x is solved as a function of the variable y. And since inverse functions swap the input and output values ​​(that is, if f (x) = y then f⁻¹(y) = x), then the variables are swapped and write the inverse as a function.

You know that he function f(x) = 2.5*x + 150 or y=2.5*x +150

Solving for x:

2.5*x +150=y

2.5*x= y-150

`x=(y-150)/(2.5)`

`x=(y)/(2.5)-(150)/(2.5)`

`x=0.4y-60=(2)/(5)y-60`

Exchanging the variable, you obtain that the inverse function of f(x)=2.5*x+150 is f⁻¹(x)=
`(2)/(5)x-60`