Question

*WILL GIVE BRAINLIEST*
Your wage is $8.00 per hour plus $0.75 for each unit you produce in an hour. The function representing your
hourly wage f(x) in terms of the number of units produced x is f(x) = 8.00 +0.75x.

Answer 1

Using function concepts, it is found that:

1. The inverse function is: $f^{-1}(x) = \frac{x - 8}{0.75}$

2. The inverse function $f^{-1}(x)$ represents the number of units produced with an hourly wage of x.

3. The hourly wage is of $15.5.

4. 19 units are produced.

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The function is:

$f(x) = 8 + 0.75x$

• The input is x, which is the number of units produced.
• The output is f(x), which is the hourly wage.
• In the inverse function, the input and the output are exchanged.

Item 1:

To find the inverse, we exchange x and y, and solve for y. Thus:

$x = 8 + 0.75y$

$0.75y = x - 8$

$y = \frac{x - 8}{0.75}$

$f^{-1}(x) = \frac{x - 8}{0.75}$

Item 2:

Exchanging the input and the output compared to the original function, the inverse function $f^{-1}(x)$ represents the number of units produced with an hourly wage of x.

Item 3:

• This is f when x = 10, thus:

$f(10) = 8 + 0.75(10) = 8 + 7.5 = 15.5$

The hourly wage is of $15.5.

Item 4:

• This is the inverse function when x = 22.25, thus:

$f^{-1}(22.25) = \frac{22.25 - 8}{0.75} = 19$

19 units are produced.

A similar problem is given at https://brainly.com/question/24437482