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.
