# Which of the following statements describes the relation shown in the table below? - -- - (look at the above numbers as if it were a table, and you.) a. it does not have an inverse since it is a relation but not a function b. it does not have an inverse since it represents a function that is not one-to-one. c. it has an inverse since it represents a function that is not one-to-one. d. it has an inverse since it represents a one-to-one function.

Identify the inverse g(x) of the given relation f(x).

f(x) = {(8, 3), (4, 1), (0, –1), (–4, –3)}

g(x) = {(–4, –3), (0, –1), (4, 1), (8, 3)}

g(x) = {(–8, –3), (–4, 1), (0, 1), (4, 3)}

g(x) = {(8, –3), (4, –1), (0, 1), (–4, 3)}

g(x) = {(3, 8), (1, 4), (–1, 0), (–3, –4)}

f(x) is a function since every x-coordinate of f(x) is different. To find the inverse of f(x), we write all ordered pairs with the x- and y-coordinates switched.

g(x) = {(3, 8), (1, 4), (-1, 0), (-3, -4)}

Now we look at g(x) and notice that every x-coordinate is different. g(x) is also a function.

Answer to the first part:

The inverse of f(x), g(x) is g(x) = {(3, 8), (1, 4), (-1, 0), (-3, -4)}

Answer to the true statement part:

g(x) is a function because f(x) is one-to-one.

It is all of the answers A,B,C,D they are all correct

Step-by-step explanation:

I just got done taking it and got it right when I clicked all of the answers

The first answer is ...

D. g(x) = {(3, 8), (1, 4), (–1, 0), (–3, –4)}

And the second answer is ...

C. g(x) is a function because f(x) is one-to-one.