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If f is one to one and f(14) =3, then f-1(3) = 14, what is the value of f-1(3)?

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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.

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