Final answer:
If the output of two function machines is the same, it means that the input for both machines is also the same.
Step-by-step explanation:
If Hazel inputs the same number into both of these function machines and the output she is given is the same for both machines, then the number she inputs must be the same.
For example, let's say the function machines are represented by the equations f(x) = 2x and g(x) = x + 4. If Hazel inputs the number 5 into both machines, the output for both would be 10, since both machines would perform the operation of multiplying the input by 2 and adding 4.
Therefore, the number Hazel inputs into both function machines is the same.