Question

Suppose that f is a continuous function such that f(3) = 8 and f(9) = 2. If f(x) is defined for each real number x, find f(6).

Answer 1

Without additional information about the continuous function f(x), the value of f(6) cannot be determined from the given data.

Step-by-step explanation:

The student is asking to find the value of f(6) given that f is a continuous function with known values at f(3) = 8 and f(9) = 2. However, without additional information about the function f(x), such as its equation or detailed behavior between x = 3 and x = 9, we cannot precisely determine the value of f(6). In continuous functions, values between known points cannot be accurately predicted without more information because they do not necessarily change at a constant rate or follow a straight line. If it were a linear function, one could interpolate, but this has not been stated in the problem. Therefore, in the current context, the answer to what f(6) equals cannot be provided.