Questions: What is the inverse of the function y-2=3 x ? (A) y=2 x/3 (B) y=(2-x)/3 (C) y=(x-2)/3 (D) y=3 x-2

Solution Steps

To find the inverse of the function \( y - 2 = 3x \), we need to follow these steps:

1. Replace \( y \) with \( f(x) \) to get \( f(x) - 2 = 3x \).
2. Solve for \( x \) in terms of \( f(x) \).
3. Replace \( f(x) \) with \( y \) and \( x \) with \( y \) to get the inverse function.

The original function is given by the equation: \[ y - 2 = 3x \]

To find the inverse, we need to express \( x \) in terms of \( y \). Rearranging the equation gives: \[ 3x = y - 2 \] Dividing both sides by 3, we find: \[ x = \frac{y - 2}{3} \]

Now, we replace \( x \) with \( y \) and \( y \) with \( x \) to express the inverse function: \[ y = \frac{x - 2}{3} \]

Final Answer