To find g'(2), we first need to find the inverse of f(x) by swapping the roles of x and y and solving for y. Then, differentiate the equation with respect to y to find g'(x), and substitute x = 2 to find g'(2) = 35.
To find g'(2), we need to first find g(x), the inverse of f(x). To find the inverse, we swap the roles of x and y and solve for y. So, we have y = x^4 + 3x - 2. Rearranging this equation to solve for x, we have x^4 + 3x - 2 = y. Now, we can solve this equation for x in terms of y.
Next, we differentiate both sides of the equation with respect to y to find g'(x). Differentiating x^4 + 3x - 2 = y with respect to y, we get 4x^3 + 3 = g'(x). Finally, substitute x = 2 into the equation to find g'(2).
So, g'(2) = 4(2)^3 + 3 = 35.