The problem asks us to find the input of a function machine, given that the machine performs the operations "subtract 3" and "add 2" sequentially, and the output is -13. We need to reverse the operations to find the original input.

1. Problem Description

The problem asks us to find the input of a function machine, given that the machine performs the operations "subtract 3" and "add 2" sequentially, and the output is -

1

3. We need to reverse the operations to find the original input.

2. Solution Steps

Let the input be $x$. The function machine performs the following operations:

First, subtract 3: $x - 3$

Then, add 2: $(x - 3) + 2$

The output is -13, so we have the equation:

$(x - 3) + 2 = -13$

Simplify the left side of the equation:

$x - 3 + 2 = -13$

$x - 1 = -13$

To solve for $x$, add 1 to both sides of the equation:

$x - 1 + 1 = -13 + 1$

$x = -12$

3. Final Answer

The input is -12.