# Equation of fusionning two graphs

So while practicing some calculus problems for a test, I felt on a relatively small but hard problem that I couldn’t even know where to start from :

The problem ask you to prove that the equation of the graph Γ\Gamma is the result of fusionning two graphs CgCg and CfC_f Given that Γ\Gamma ‘s equation is as follows :

xآ²yآ²−2xآ²y+xآ²−2x+1=0 xآ²yآ² – 2xآ²y + xآ² – 2x + 1 = 0

And that :

f(x) = \frac{x + \sqrt{2x – 1}}{x} f(x) = \frac{x + \sqrt{2x – 1}}{x}

g(x) = \frac{x – \sqrt{2x – 1}}{x} g(x) = \frac{x – \sqrt{2x – 1}}{x}

And by fusionning two graphs I mean that when two graphs get closer togethr until they form one graph . (I couldn’t find the right term in english, given that I study maths generally in arabic ) .

I really don’t have any idea on how to approach this kind of problem, I’m not looking for raw answers, I’m looking for explanation and I’d appreciate if you could give an example 🙂 .

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Are you sure there is not a typo in ff, gg? Without the factor of 2 outside the square root, ff and gg would be what you get by solving for yy the first equation. In that case the first equation would be a curve in the (x,y)(x,y)-plane which can be written as the superposition of the graphs of ff and gg, with no “fusioning” needed.
– GFR
2 days ago

@GFR Ouupps, my fault for the 2 edited .
– Anis Souames
2 days ago

Good! Is my comment clear or should I elaborate?
– GFR
2 days ago

@GFR So If I understand, I need to solve the 1st equation and I get two solutions, one is f(x) and the other is g(x) ? I’d love if you could elaborate it a bit more in an answer 🙂 .
– Anis Souames
2 days ago

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