Answer:
Let's solve the problems one by one:
1. f(2): We substitute x = 2 into the function f(x) = 12x. So, f(2) = 12 x 2 = 24.
2. f−1(1): We substitute x = 1 into the function f−1(x) = 2x. So, f−1(1) = 2 x 1 = 2.
3. f−1(f(2)): First, we find f(2) which we have already calculated as 24. Then we substitute this into f−1(x), so f−1(24) = 2 x 24 = 48.
So, f(2) = 24, f−1(1) = 2, and f−1(f(2)) = 48.
Explanation:
The notation "f^-1" is used to denote the **inverse function** of a given function "f". If "f" takes an input "x" and produces an output "y", then the inverse function "f^-1" takes "y" as an input and produces "x" as an output. In other words, the inverse function "undoes" the operation of the original function.
For example, if we have a function f(x) = 2x, its inverse function would be f^-1(x) = x/2. This is because if you put a number into f(x) and then put the result into f^-1(x), you will get back the original number.
In your case, f(x) = 12x and f^-1(x) = 2x are given as the function and its inverse.