Final answer:
When a one-to-one function f satisfies f(14) = 3, the inverse function f^-1(3) equals 14, because the input that results in an output of 3 is 14.
Step-by-step explanation:
If f is a one-to-one function and is given that f(14) = 3, then to find the
value of f-1(3), we are essentially looking for the input value that results in
the output of 3.
Since f is one-to-one, each output is the result of a unique input.
Therefore, the process of finding an inverse is like 'reversing' the function. When we know that f(14) = 3, by the definition of an inverse
function, we have that f-1(3) = 14. Therefore, the value of f-1(3) is indeed 14.