Question

If F(x) = x-3, which of the following is the inverse of F(x)?

O A. F1(x) = x+ 3
B. F¹(x) = 3x
OC. F¹(x) = x-3
OD. F¹(x) = 3-x

Answer 1

The inverse of the function F(x) = x - 3 is found by switching x and y and then solving for y, which gives F¹(x) = x + 3.

Step-by-step explanation:

The student has asked about finding the inverse function for a given function F(x) = x - 3. To find the inverse of a function, you need to solve for the variable x in terms of the input of the original function. This involves switching the roles of x and y, then solving for y again to get the inverse function.

Let's set F(x) to y for easier calculation, so we have y = x - 3. To find the inverse, we switch x and y to get x = y - 3, and then solve for y to find the inverse function.

Adding 3 to both sides of the equation, we get: x + 3 = y, which when written in function form becomes F¹(x) = x + 3.

Therefore, the correct option for the inverse of F(x) is:

• A. F¹(x) = x + 3