Final answer:
Since the one to one function f produces an output of 7 for an input of 2, the inverse function f^(-1)(7) will yield an input of 2.
Step-by-step explanation:
If a function f is one to one, every output is uniquely paired with one input. Since we know that f(2)=7, in a one to one function, no other input can have the output of 7, likewise, 2 is the only input that will give an output of 7.
Therefore, when we're finding the inverse of the function, denoted as f-1, we're essentially finding the input that corresponds to a given output. In other words, f-1(7) is asking us 'for what input value does the function f give an output of 7?'. Since we know f(2)=7, then it follows that f-1(7)=2.