Question

Problem: Gerri made a function machine. Find the rule for Gerri's function machine.

-1 Goes in -1 Comes Out. What functions went on?

Answer 1

There are an infinite number of possibilities, and not enough information
to decide which possibility is really the one inside the function machine.

Here are a few. Each of these gives the result that you described,
and there are an infinite number of others:

f(x) = x

f(x) = 2x + 1

f(x) = 10x + 9

f(x) = x² - 2

f(x) = 7x² - 8

f(x) = 31x³ + 30

f(x) = log( |x| ) - 1

f(x) = ln( |x| ) - 1

f(x) = x tan(45°)
.
.
etc.