jmc

Question

Suppose the function f has all real numbers in its domain and range and is invertible. Some values of f are given by the following table: arrayc || c | c | c | c | c x & 1 & 2 & 3 & 4 & 5 f(x) & 2 & 3 & 5 & 7 & 8 arrayWhat is the value of f(f(3)) + f(f^-1(4)) + f^-1(f^-1(5))? If there is not enough information to answer this question, enter "NEI".

Accepted Answer

Reading the table, we see that f(f(3)) = f(5) = 8. Although we can't look up f^-1(4) in the table, we know that f(f^-1(4)) = 4, since f(f^-1(x))=x for all x (by the definition of an inverse function). Since f(3) = 5, we have f^-1(5) = 3, and so f^-1(f^-1(5)) = f^-1(3).Then, since f(2) = 3, we have f^-1(f^-1(5)) = f^-1(3) = 2.Combining the information above, we get f(f(3)) + f(f^-1(4)) + f^-1(f^-1(5)) = 8+4+2 = 14.