If the function defined by the following is onetoone complet

If the function defined by the following is one-to-one, complete parts a through c. f(x) = 8/x - 3, x notequalto 3 What is the equation for the inverse function? Select the correct choice below, and fill in the answer box if necessary. The function is one-to-one. f^-1 (x) =, x notequalto 0. (Simplify your answer.) The function is not one-to-one. If the function is one-to-one, graph f and f^-1 on the same axes. Choose the correct graph below. Give the domain and range of f. Select the correct choice below, and fill in the answer boxes if necessary. The domain of f is and the range of f is. (Type your answers in interval notation.) The function is not one-to-one. Give the domain and range of f^-1. Select the correct choice below, and fill in the answer boxes if necessary. The domain of f^-1 is and the range of f^-1 is. (Type your answers in interval notation.) The function is not one-to-one.

Solution

a. f(x)=8/(x-3)

First we write f(x) as y and then switch x and y

x=8/(y-3)

x/8=1/y-3

8/x=y-3

y=8/x    +3

f^-1(x)= 8/x   + 3

Graph A is the correct graph

c. domain

IN rational expression bottom cant be zero and at x=3 it is zero

Therefore domain is (-inf,3)U(3,infinity)

the domain of the inverse function is the range of the given function

And as we see that the domain of the inverse function is (-inf,0)U(0,inf)

And that\'s the range