Suppose f(g(x)) = x, such that f and g are differentiable. If f(1) = 3 and f ′(1) = 2, determine the value of g′(3). Homework Help ✎
Recall that f(g(x)) = x is the definition of inverse functions. In other words, you are being told that f(x) and g(x) are inverses.
Inverse functions have reciprocal slopes at corresponding (x, y)→(y, x) values.