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Given f(x) = (x + 1)² for x >= -1, let g(x) be the function whose graph is the mirror image of the graph of f across the line y = x. Find g(x).

1. -sqrt(x) - 1, x >= 0
2. 1/(1 + x)², x >= -1
3. sqrt(x + 1), x >= -1
4. sqrt(x) - 1, x >= 0

Correct answer: sqrt(x) - 1, x >= 0

Solution

Reflecting a graph in y = x produces the inverse function. Invert y = (x+1)² on the domain x >= -1 (where x + 1 >= 0), giving g(x) = sqrt(x) - 1 with domain x >= 0.

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