Choose a true statement. g(x) is not a function because f(x) is not a function. g(x) is not a function because f(x) is not one-to-one. g(x) is a function because f(x) is one-to-one. g(x) is a function because f(x) is not one-to-one.

The inverse of a one-to-one function is also a one-to-one function. g(x) is a function because f(x) is one-to-one.

Given that:

g(x) is the inverse function of f(x). So, we have:

To determine if g(x) is a function; we use the following illustration to describe the elements of f(x).

We have:

In the above illustration, each value of x have one corresponding y value.

This means that

Base on the above analysis, we can conclude that (c) is true

Read more about functions and inverse at:

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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.