f(x) = (x-1)^2 for x 1 , g(x) is a function whose graph is the reflection of the graph of f(x) in the line y = x , then g(x) is

Step-by-step solution

The graph of g(x) is the reflection of the graph of f(x) in the line y = x , which means g(x) is the inverse function of f(x) . Let y = f(x) = (x-1)^2 for x 1 . Taking the square root on both sides, we get: y = |x-1| Since x 1 , we have x-1 0 , so |x-1| = x-1 . y = x - 1 x = y + 1 Interchanging x and y to find the inverse function, we get: y = x + 1 Therefore, g(x) = x + 1 . Answer: x + 1