Question

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

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

Answer 1

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 2nd question:

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.

Explanation:

Answer 2

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

Explanation:

A simple property of inverse functions is that:

Whenever a function/relation is given in the form of ordered pair such as:

f(x) = (a,b), (c,d)

the inverse of that, e.g. g(x), would be simply changing the first and second values (interchange). Thus

g(x) = (b,a), (d,c)

So, from the relation f(x) given, if we change the first and 2nd values, we would get:

{(3, 8), (1, 4), (-1,0), (-3, 4)

This is the 4th answer choice, hence that is correct.