Question

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)} \\)

Explanation:

To find the inverse of a relation given as a set of ordered pairs, we swap the \(x\)- and \(y\)-values of each ordered pair. For the relation \(f(x)=\{(8, 3), (4, 1), (0, -1), (-4, -3)\}\), swapping the coordinates of each pair:

• For \((8, 3)\), the inverse pair is \((3, 8)\).
• For \((4, 1)\), the inverse pair is \((1, 4)\).
• For \((0, -1)\), the inverse pair is \((-1, 0)\).
• For \((-4, -3)\), the inverse pair is \((-3, -4)\).

So the inverse relation \(g(x)\) should be \(\{(3, 8), (1, 4), (-1, 0), (-3, -4)\}\).

Answer:

D. \(g(x)=\{(3, 8), (1, 4), (-1, 0), (-3, -4)\}\)