Final answer:
To find f(f−1(6)), identify the x-value that corresponds to f(x) = 6 from the table, which is 1. Then use that x-value to find f(1) from the table, which is 6. Therefore, f(f−1(6)) equals 6.
Step-by-step explanation:
The student has provided a table of values for a one-to-one function and needs to find f(f−1(6)). The first step is to identify the value f−1(6), which refers to the x-value for which f(x) = 6. Looking at the provided table, when x = 1, f(x) = 6. So, f−1(6) = 1. The next step is to substitute this x-value back into the function to find f(1). From the table, f(1) equals 6. Thus, f(f−1(6)) = f(1) = 6. This has been a step-by-step explanation of evaluating the composite function.