Question

This is a 4 part question as u can see in directions please help I’m stuck on this question on my homework

Answer 1

Given the function:

`f\left(x\right)=3x-8`

a) the inverse function is:

`f^(-1)\left(x\right)=(1)/(3)(x+8)`

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:

`f^(-1)^:\text{ }\Re\rightarrow\Re`