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 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.

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) }

Answer:

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.