Which of the following domain restrictions should be used for
the function f(x) = x2 + 4x + 4 so that it will have an inverse function?

Question

mathmate · Answer

For an inverse to exist, the function must be one-to-one and onto (bijective).  Geometrically, it means that it must pass both the horizontal and vertical line tests.

If the domain is limited to the half-plane on either side of the vertex, it will have an inverse.

The function is x2 + 4x + 4 = (x+2)^2, so the vertex passes through x=-2.

Therefore, by limiting the domain to (-inf, -2] or [-2,inf) , the function will have an inverse.

mathmate · Answer

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