This notation means that when the input of the function f is 1, the output is 2.
This notation means that the derivative of the function f at the input 1 is 3.
This notation means that the derivative of the function f at the input 2 is 4.
f^-1(2) is the inverse of the function f evaluated at the output 2. In other words, it is the input that produces the output of 2 when put into the inverse function.
To find f^-1(2), we can use the formula f^-1(x) = (f'(x))^(-1), where x is the input that produces the output of 2. In this case, since f(1) = 2, we can substitute 1 for x and use the given derivative values to solve for f^-1(2). This gives us f^-1(2) = (3)^(-1) = 1/3.