Question

How to find the inverse of functions.

A) Swap x and y
B) Divide by x
C) Take the square root
D) Add the reciprocal

Answer 1

To find the inverse of a function, swap x and y, solve for y, and finalize the inverse function.

Step-by-step explanation:

When finding the inverse of a function, there is a general process to follow:

1. Swap x and y: Replace y with x and x with y in the original function.
2. Solve for the new y: Rearrange the equation to isolate y.
3. Finalize the inverse function: Replace y with the inverse function notation, usually represented as f-1(x).

Here is an example to illustrate the process. Let's say we have the function f(x) = 2x + 3 and we want to find its inverse:

1. Swap x and y: Replace f(x) with x and x with y, giving us x = 2y + 3.
2. Solve for the new y: Rearrange the equation to isolate y: y = (x - 3) / 2.
3. Finalize the inverse function: Replace y with f-1(x), giving us f-1(x) = (x - 3) / 2.

So the inverse function of f(x) = 2x + 3 is f-1(x) = (x - 3) / 2.