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identify the inverse g(x) of the given relation f(x). f(x) = {(8, 3), (4, 1), (0, –1), (–4, –3)} a. g(x) = {(–4, –3), (0, –1), (4, 1), (8, 3)} b. g(x) = {(–8, –3), (–4, 1), (0, 1), (4, 3)} c. g(x) = {(8, –3), (4, –1), (0, 1), (–4, 3)} d. g(x) = {(3, 8), (1, 4), (–1, 0), (–3, –4)}

Verified Answer :

dalendrk

\(f(x)\to\{(8;\ 3);\ (4;\ 1);\ (0;-1);\ (-4;-3\}\\\\f^{-1}(x)\to\{(3;\ 8);\ (1;\ 4);\ (-1;\ 0);\ (-3;-4)\}\)

Answer:

The correct option is 4.

Step-by-step explanation:

The given relation is

\(f(x)=\{(8, 3), (4, 1), (0, -1), (-4, -3)\}\)

We need to find the inverse g(x) of the given relation f(x).

If a relation is defined as

\(R=\{(x,y):x\in R,y\in R\}\)

then inverse of the relation is defined as

\(R^{-1}=\{(y,x):x\in R,y\in R\}\)

\(f^{-1}(x)=\{(3,8), (1,4), (-1,0), (-3,-4)\}\)

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

The inverse of given relation is g(x) = {(3, 8), (1, 4), (–1, 0), (–3, –4)}.

Therefore the correct option is 4.

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