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I have a question about how to obtain an equation of an inverse function.

The equation is $y=x^2+2x+3$ and I changed $x$ and $y$ to get $x=y^2+2y+3$ and it is only a matter of rearranging to have $y$ on the left side but I am finding it difficult to do so.

I got $y(y+2)=x-3$ but since there are 2 of the $y$ on one side I am unsure how to make $y$ the subject.

I have googled for solutions and they had $y$ on both sides, how would I have $y$ as a subject?

MathsGoogle
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    Have you tried the quadratic formula? – Ertxiem - reinstate Monica Mar 20 '19 at 01:22
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    Hint. Use the quadratic formula to solve $x^2 + 2x +3 - y = 0$ for $x$ in terms of $y$. There will be two solutions - think through what that means. – Ethan Bolker Mar 20 '19 at 01:23
  • I find it far more convenient to instead think of completing the square, and so writing it as $(y^2+2y+1)+2 = x$ which after factoring becomes $(y+1)^2 = x-2$. That being said, the function is technically not invertible (if you continue, you'll have a pesky $\pm$ symbol to deal with and the "inverse" function won't pass the vertical line test) – JMoravitz Mar 20 '19 at 01:26
  • Complete the square. You’re on the right track. – MPW Mar 20 '19 at 01:27
  • Ah, so is it the best to complete the square if I have these kinds of problems? I tried quadratic formula and I got $-1±sqrt(x-2)$. – MathsGoogle Mar 20 '19 at 01:46
  • Complete the square, quadratic formula, doesn't matter, whichever floats your boat. You get the same answer either way (if you don't muck up the algebra). – Gerry Myerson Mar 20 '19 at 02:46

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