Final answer:
The inverse of the function y = 3/2x - 2 is y = 2/3x + 4/3. The closest option provided, with potential for a typo, is y = 2/3x + 2, which is option a.
Step-by-step explanation:
The question asks for the inverse of the function given by the equation y = \frac{3}{2}x - 2. To find the inverse of a function, we swap the x and y variables and solve for y. Here are the steps:
- Replace y with x to get x = \frac{3}{2}y - 2.
- Add 2 to both sides to isolate the term with y, resulting in x + 2 = \frac{3}{2}y.
- Multiply both sides by \frac{2}{3} to solve for y, which gives us y = \frac{2}{3}x + \frac{4}{3}.
Therefore, the equation that represents the inverse of the function y = \frac{3}{2}x - 2 is y = \frac{2}{3}x + \frac{4}{3}. None of the options given exactly matches this equation, suggesting a potential typo in the provided options. However, if the options provided are not typos, the closest to the correct answer would be option a. y = \frac{2}{3}x + 2, considering the constant term. This option does not have the correct constant, but it has the correct coefficient for x.