The function f(x)=x^2 + 2 is not one-to-one. Determine a restricted domain that makes it one-to-one, and find the inverse.
+129839 f(x) = x^2 + 2 for f(x), write y
y = x^2 + 2 get x by itself
y - 2 = x^2 take the positive and negative square roots of both sides
± √ [y - 2] = x "swap" x and y
± √ [x - 2] = y for y, write f-1(x)
± √ [x - 2] = f-1(x)
If we restict the original function to the domain ( -inf, 0), then - √ [x - 2] is the inverse function
If we restrict the original function to the domain (0, inf) then + √ [x - 2] is the inverse function
Note : "0" can belong to either of the original domains and either of the inverse domains
