154k views
5 votes
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);

User Oko
by
7.6k points

2 Answers

4 votes

Answer:

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:

User Simon Groenewolt
by
8.0k points
4 votes

Answer:

"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.

User Ingo Leonhardt
by
8.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories