Problem

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

Answer

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Answer

Next, substitute \(x = \frac{y + 2}{3}\) into the first relation to get \(y = 3(\frac{y + 2}{3}) - 2 = y\).

Steps

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 \(y = 3(\frac{y + 2}{3}) - 2 = y\).

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