Question

Jake earns $7.50 per hour working at a local car wash. The function, ƒ(x) = 7.50x, relates the amount Jake earns to the number of hours he works. Write the inverse of this relation.

Answer 1

If you want to create an inverse, just simply swap x and y and solve for y

x = 7.5y

x/7.5 = y

y = x/7.5

f^-1(x) = x/7.5

Answer 2

`f^(-1) (x)` =
`(x)/(7.50)`

Explanation:

Jake earns $7.50 per hour working at a local car wash.

The function, f(x) = 7.50x relates the amount jake earns to the number of hours he works.

Now we have to write the inverse of this function.

To determine the inverse of this function we will rewrite the function in an equation form.

Then swap x with y and then we will solve the equation for y.

Since f(x) = 7.50x

or y = 7.50x

Swapping of x and y

x = 7.50y

y =
`(x)/(7.50)`

Now we will write it in the form of a function.

`f^(-1) (x)` =
`(x)/(7.50)`

Therefore, inverse function will be
`f^(-1) (x)` =
`(x)/(7.50)`