Final answer:
If f is a one-to-one function and f(5)=9, then f^-1 (9)=5.
Step-by-step explanation:
A one-to-one function, also known as an injective function, is a function where each element in the domain maps to a unique element in the codomain.
Since f is one-to-one and f(5)=9, it means that the input value 5 is mapped to the output value 9.
To find f-1(9), we simply need to reverse the roles of the input and output values.
So, f-1(9) would be equal to the input value that maps to 9. In this case, it is 5, since f(5)=9.
Therefore, f-1(9)=5.