Determine if the relation (y = 3x - 2) is the inverse of the relation (x = frac{y + 2}{3}).

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Accepted Answer

Step:1 ：To check if two relations are inverses of each other, we can apply the composite of the two functions in both orders and see if the result simplifies to x in both cases.Step:2 ：First, substitute (y = 3x - 2) into the second relation to get (x = frac{(3x - 2) + 2}{3} = x).Step:3 ：Next, substitute (x = frac{y + 2}{3}) into the first relation to get (y = 3(frac{y + 2}{3}) - 2 = y).

Answer

Step: 1 ：To check if two relations are inverses of each other, we can apply the composite of the two functions in both orders and see if the result simplifies to x in both cases.Step: 2 ：First, substitute (y = 3x - 2) into the second relation to get (x = frac{(3x - 2) + 2}{3} = x).Step: 3 ：Next, substitute (x = frac{y + 2}{3}) into the first relation to get (y = 3(frac{y + 2}{3}) - 2 = y).

Determine if the relation $y = 3 x - 2$ is the inverse of the relation $x = \frac{y + 2}{3}$ .

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Popular Problems

Determine if the relation y=3x−2 is the inverse of the relation x=y+23.

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Popular Problems

Determine if the relation $y = 3 x - 2$ is the inverse of the relation $x = \frac{y + 2}{3}$ .