To find the value of g(2), where g is the inverse function of f, we need to first understand what it means for a function to have an inverse. If g is the inverse of f, it means that for every x in the domain of f, f(g(x)) = x and g(f(x)) = x.
In simpler terms, applying function f to g(x) returns x, and vica-versa. To determine g(2), we actually need to find the value of x such that f(x) = 2. Once we find this x, we will know that g(2) is equal to that x.
So, the values of g(2) depend on the specific function f. For instance, if f(x) = x + 1, we need to solve the equation:
f(x) = 2
x + 1 = 2
x = 1
This tells us that g(2) = 1, since applying f to 1 gives us 2. If the function were different, the result would change accordingly. Therefore, to find g(2), always solve for f(x) = 2 for the specific form of function f you are using.