Given the function:
[tex]f\left(x\right)=3x-8[/tex]
a) the inverse function is:
[tex]f^{-1}\left(x\right)=\frac{1}{3}(x+8)[/tex]
So, we have two linear functions, which are one-to-one (every element of the function's codomain is the image of at most one element of its domain).
b) In order to graph both functions, keep in mind that f is a line with slope 3 and y-intercept at y = -8. As for f^{-1} it is a line with slope 1/3 and y-intercept at y = 8/3. You can simply graph both function on the same axes by calculating the values of f and f^{-1} given some values of x, for instance:
x = ..., -2 , -1, 0, 1, 2,...
f(x) =
f^{-1} =
As can be seen in the following graph: purple line represents f and pink line represents f^{-1}:
c) The domain and range of f(x) and f^{-1} is the same:
[tex]f:\text{ }\Re\rightarrow\operatorname{\Re}[/tex][tex]f^{-1}^:\text{ }\Re\rightarrow\Re[/tex]
