1. The problem asks us to find the input value of a function machine that produces an output of 42 after passing through an intermediate value of -34. 2. We start by understanding the function machine steps: the input goes to -34, then from -34 to 42. 3. Let the input be $x$. The function machine transforms $x$ to -34, so the first function is $f(x) = -34$. 4. The second transformation takes -34 to 42, so the second function is $g(-34) = 42$. 5. Since the first function outputs -34 regardless of $x$, the input $x$ must be such that $f(x) = -34$. 6. Therefore, the input $x$ is the value that the function machine takes to produce -34, which is the unknown we want. 7. Since the problem does not provide the explicit function, but shows the input leads to -34, the input is simply the value that maps to -34. 8. Hence, the input is the value that when processed by the function machine gives -34, which is the unknown input. 9. The final answer is the input value that leads to -34, which is the unknown question mark in the diagram. Since the problem does not provide a formula, the input is the unknown value that produces -34 as output in the first step.