What is the inverse function of f(x) = (3x - 2)/4?

What is the inverse function of f(x) = (3x - 2)/4?

• A. f^(-1)(x) = (2 + 4x)/3
• B. f^(-1)(x) = (4x + 2)/3
• C. f^(-1)(x) = (3x + 2)/4
• D. f^(-1)(x) = (3x - 4)/2

Answer: (B)

To find the inverse function of f(x) = (3x - 2)/4, we need to follow a systematic approach. The first step involves replacing f(x) with y: y = (3x - 2)/4. Next, we swap the roles of x and y to prepare for finding the inverse: x = (3y - 2)/4. Now, to isolate y, we will first eliminate the fraction by multiplying both sides by 4: 4x = 3y - 2. Adding 2 to both sides yields: 4x + 2 = 3y. Now, to solve for y, we divide both sides by 3: y = (4x + 2)/3. Thus, we have found that the inverse function is expressed as: f^(-1)(x) = (4x + 2)/3. This confirms that the correct choice matches our derived inverse function, affirming its accuracy. Understanding these steps is crucial since it highlights the process of finding inverse functions, which typically involves swapping variables and solving for the new dependent variable.

To find the inverse function of f(x) = (3x - 2)/4, we need to follow a systematic approach. The first step involves replacing f(x) with y:

y = (3x - 2)/4.

Next, we swap the roles of x and y to prepare for finding the inverse:

x = (3y - 2)/4.

Now, to isolate y, we will first eliminate the fraction by multiplying both sides by 4:

4x = 3y - 2.

Adding 2 to both sides yields:

4x + 2 = 3y.

Now, to solve for y, we divide both sides by 3:

y = (4x + 2)/3.

Thus, we have found that the inverse function is expressed as:

f^(-1)(x) = (4x + 2)/3.

This confirms that the correct choice matches our derived inverse function, affirming its accuracy. Understanding these steps is crucial since it highlights the process of finding inverse functions, which typically involves swapping variables and solving for the new dependent variable.