Question

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.

Answer 1

Complete question is

state a reasonable domain for the problem statement, find the inverse function .

Answer :

f(x) = 9x

For all linear function the domain and range is all real numbers

Here x is his jogging time in hours. time cannot be negative .

Domain is [0, ∞)

Range y is total distance he has traveled. Distance cannot be negative

Range is [0, ∞)

Now we find the inverse function for f(x)

f(x) = 9x

Replace f(x) with y

y= 9x

Replace y with x and x with y

x = 9y

Solve for y

`(x)/(9) = y`

`y = (x)/(9)`

Now replace y with f^-1(x) to get the inverse function

`f^-1(x) = (x)/(9)`