Final answer:
To solve (f^(-1))[(f^(-1))(-1)], we first find the inverse function f^(-1)(x) which is (x + 7) / 3. Then, we compute f^(-1)(-1) and use that result in f^(-1)(x) again to find the final answer, which is 1. The correct answer is C. 1
Step-by-step explanation:
The question is asking to find the value of the expression (f(-1))[(f(-1))(-1)] where f(x) = 3x - 7. To do this, we first need to find the inverse function f(-1)(x) which will undo the operation done by f(x).
To find f(-1)(x), we set f(x) = y which gives us y = 3x - 7. Then, to solve for x as a function of y, we swap x and y and solve the resultant equation for x, which gives us x = (y + 7) / 3. So f(-1)(x) = (x + 7) / 3.
Then we plug in the value -1 into f(-1)(x) to find f(-1)(-1) which computes to (-1 + 7) / 3 = 2. Now we use the value just found and plug it in again to find (f(-1))(2), which gives us (2 + 7) / 3 = 3. Therefore, the correct answer is C. 1.