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Reversing a function machine

Undo each operation in reverse order.

  • Start with the known output and work backwards.
  • Use inverse operations: undo addition by subtraction and multiplication by division.
  • Reverse the order of the operations. Check the input by running the original machine forwards.

Example 1

Find the input . Work backwards through the function machine.

InputOutput
Apply each operation from input to output.
Undo the last operation first, then divide.Simplify the numerical terms and collect like terms.

Example 2

Find the input . Work backwards through the function machine.

InputOutput
Apply each operation from input to output.
Undo the last operation first, then divide.Simplify the numerical terms and collect like terms.

Your turn

Question 1

Find the input . Work backwards through the function machine.

InputOutput
Apply each operation from input to output.
Check answer
InputOutput
Work backwards using inverse operations.
Undo the last operation first, then divide.Simplify the numerical terms and collect like terms.
Question 2

Find the input . Work backwards through the function machine.

InputOutput
Apply each operation from input to output.
Check answer
InputOutput
Work backwards using inverse operations.
Undo the last operation first, then divide.Simplify the numerical terms and collect like terms.
Question 3

Find the input . Work backwards through the function machine.

InputOutput
Apply each operation from input to output.
Check answer
InputOutput
Work backwards using inverse operations.
Undo the last operation first, then divide.Simplify the numerical terms and collect like terms.
Question 4

Find the input . Work backwards through the function machine.

InputOutput
Apply each operation from input to output.
Check answer
InputOutput
Work backwards using inverse operations.
Undo the last operation first, then divide.Simplify the numerical terms and collect like terms.
Question 5

Find the input . Work backwards through the function machine.

InputOutput
Apply each operation from input to output.
Check answer
InputOutput
Work backwards using inverse operations.
Undo the last operation first, then divide.Simplify the numerical terms and collect like terms.
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