SOLUTION: Determine whether f(x)=x^2-3 has inverses?

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Question 427828: Determine whether f(x)=x^2-3 has inverses?
Found 2 solutions by richard1234, robertb:
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) has an inverse, but it is not a function. This is because a horizontal line can be drawn intersecting f(x) at two points, so when the graph is rotated about y = x, a vertical line can be drawn through the inverse of f(x) intersecting at two points.

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The function f%28x%29+=+x%5E2+-3 has no inverse, because it is not one-to-one. (Only one-to-one functions can have inverses. One-to-one functions are those such that f%28x%5B1%5D%29+=+f%28x%5B2%5D%29 implies x%5B1%5D+=+x%5B2%5D.) To enable the function to have an inverse, restrict its domain enough so that it will be one-to-one. (Like restricting it to [0, infinity), or a smaller subinterval to this.)