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Question 855435: Can quadratic functions be invertible?
For example f(x)=4x^2+12x+9
Please give the steps.
Answer by josgarithmetic(39621)   (Show Source):
You can put this solution on YOUR website! Each side of that function can be inverted, but the entire f(x) itself does not have an inverse. The left side of f(x) has an inverse; the right side of f(x) has another inverse.
(0) Identify the vertex of f(x). You will have x=h.
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(1) Switch f(x) for x, and then give f(x) a new name, such as g(x). Solve the equation for g(x), and put into standard form (using Completing The Square).
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(2) Identify the vertex. (It will be different than x=h) (helps in sketching).
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(3) The f(x) branch where x<=h will correspond the the lower branch of g(x);
The f(x) branch where x>=h will correspond the the upper branch of g(x).
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