Function machines

Foundation and Higher

The idea

A function machine applies operations in order. To go backwards, undo each operation in reverse order: the inverse of $\times 3$ then $+ 4$ is $- 4$ then $\div 3$ .

Write the operations in order.
Swap each for its inverse.
Apply the inverses from the end back to the start.

Watch out Undo the last operation first.

See it worked

Worked exampleCalculator allowed2 marks

A function machine multiplies an input by 4, then subtracts 7. Its output is 21. What was the input?

$21+7$
Undo subtraction by adding 7: 21 + 7 = 28.
Undo multiplication by dividing by 4: 28 $\div$ 4 = 7.

Answer 7

Your turn

Question 1Non-calculator4 marks

Here is a number machine: input $\rightarrow$ multiply by 4 $\rightarrow$ subtract 7 $\rightarrow$ output.

(a) Work out the output when the input is 5.

(b) Work out the input when the output is 29.

Question 2Non-calculator2 marks

A number machine subtracts 7 and then divides by 5. The output is 9. Find the input.

Question 3Non-calculator5 marks

A function machine halves the input and then subtracts 3.

(a) Write an expression for the output when the input is x.

(b) The output is −1. Find the input.

In past papers

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