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
[tex]\frac{x}{9} = y[/tex]
[tex]y = \frac{x}{9}[/tex]
Now replace y with f^-1(x) to get the inverse function
[tex]f^-1(x) = \frac{x}{9}[/tex]
