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what domain restriction should be used for the function f(x) = x2 - 6x + 9 so that it will have an inverse function?

Mathematics
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Find the vortex of the equation as you can tell it is a parabola, then restrict the domain so it can pass the horizontal line test The horizontal line test dictates that a line drawn across a graph should not intersect the line more than once. For a function to have an inverse it must pass this test
\[f(x)=x^2-6x+9=(x-3)^2.\]Obviously, \(f:[3,\infty)\to\mathbb{R}\) or \(f:(-\infty,3]\to\mathbb{R}\).
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Hint the x coordinated for the vertex can be found by inputting a = 1 b = -6 into the equation -(b/a(2)) = x coordinate
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