Question

For problems 7–10, state a reasonable domain for the problem statement, find the inverse function f –1(x), and identify the independent and dependent quantities of the inverse.

7. Gary is jogging. The total distance he has traveled, in miles, can be estimated using the function f(x) = 9x, where x is his jogging time in hours.

8. Camryn sells computers. She earns commission for her computer sales plus a fixed wage for each day she works. Her daily earnings, in dollars, can be estimated using the function f(x) = 0.15x + 50, where x represents her computer sales in dollars.

9. The distance a motorboat travels, in meters, can be estimated using the equation f(x) = 1.9x2, wherexisthetimeinseconds,for0≤x≤10.

10. A rock band is selling tickets to a concert at a theater. The band earns money for each ticket sold, but has to pay some of the earnings to the theater. The total money earned by the band can be estimated using the function f(x) = 7.5x – 300, where x is the number of tickets sold.

Answer 1

Explanation:

7) f(x)=9x,

Here x =time logged in and hence cannot be negative

So domain = [0,∞)

`f^(-1) (x)=(x)/(9)` where here independent variable is distance the dependent is his jogging time.

8)
`f(x)=0.15x+50`

Even when x=0, f(x) =50

So domain is [50,∞)

`f^(-1) (x)=(x-50)/(15)`

Here independent variable is daily earnings and dependent variable is her computer sales in dollars

9)
`f(x)=1.9x^(2)`

Here domain =[0,10] (given)

`f^(-1) (x) = \sqrt{(x)/(9) }`

In the inverse independent variable is distance travelled and dependent is time in seconds.

10)
`f(x)=7.5x-300`

Domain =[0,∞)

`f^(-1) (x)=(x+300)/(7.5)`

Here independent variable is total money earned and x number of tickets sold