Question

What is the inverse of the function f(x) = 3x - 2?

a) f^(-1)(x) = 3x - 2
b) f^(-1)(x) = 3x + 2
c) f^(-1)(x) = (x - 2) / 3
d) f^(-1)(x) = (x + 2) / 3

Answer 1

The inverse function of f(x) = 3x - 2 is found by swapping x and y in the original equation, then solving for y, leading to the answer d) f^(-1)(x) = (x + 2) / 3.

Step-by-step explanation:

To find the inverse function of f(x) = 3x - 2, we need to perform a series of steps to solve for the new function f-1(x) which will give us the original input when we apply it to the output of f(x).

The steps are as follows:

1. Replace f(x) with y: y = 3x - 2
2. Swap x and y: x = 3y - 2
3. Solve for y: add 2 to both sides x + 2 = 3y, and then divide by 3: (x + 2) / 3 = y
4. Rewrite y as f-1(x): f-1(x) = (x + 2) / 3

Therefore, the correct inverse function is d) f-1(x) = (x + 2) / 3.