Question

The function f(x) can be described as multiplying the input x by 4 and then subtracting 3 from 4x. Which of the following would correctly describe the inverse function of f(x)?

a. Multiplying x by 3 and subtracting 4 from 3x
b. Dividing x by 4 and then adding 3 to x/4
c. Dividing x by 3 and then adding 4 to x/3
d. Adding 3 to x and then multiplying (x + 3) by 4
e. Adding 3 to x and then dividing (x + 3) by 4.

Answer 1

The correct answer is option b, which involves adding 3 to x and then dividing the result by 4 to obtain the inverse function of f(x).

Step-by-step explanation:

The correct answer is option b. To find the inverse function of f(x), you need to reverse the operations done by f(x). Since f(x) multiplies the input by 4 and then subtracts 3, to find f-1(x), you should do the opposite operations in the reverse order.

So instead of subtracting 3, you add 3, and instead of multiplying by 4, you divide by 4. This leads to the inverse function being: take the input x, add 3 to it, and then divide the result by 4.

To clarify why option b is correct, let's use an algebraic approach:

• Start with y = 4x - 3.
• Add 3 to both sides to get y + 3 = 4x.
• Divide both sides by 4 to isolate x, resulting in (y + 3)/4 = x or x = (y + 3)/4.

Therefore, the inverse function f-1(x) is obtained by adding 3 to x and then dividing the result by 4, which confirms that option b is the correct description of the inverse function.