What is f(x)(f(x))=x^2+1 ?

The solution to f(x)(f(x))=x^2+1 is Hyperbola with (h,k)=(0,0),a=1,b=1

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f(x)(f(x))=x^2+1

f (x) (f (x)) = x^{2} + 1

(h, k) = (0, 0), a = 1, b = 1

Solution steps

yy = x^{2} + 1

Rewrite

yy - x^{2} - 1 = 0

in the form of a standard hyperbola equation

\frac{( y - 0 ) ^{2}}{1 ^{2}} - \frac{( x - 0 ) ^{2}}{1 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = 1, b = 1

y^{2} - 2 y - (x^{2} - x - 1) = 0

4 x^{2} + 4 y^{2} - 9 + 18 y - 9 x^{2} = 0

4 x^{2} + 16 x - 9 y^{2} + 18 y = 29

x^{2} - 4 x - 2 y^{2} = 0

3 y^{2} - x^{2} + 18 y - 4 x + 20 = 0

What is f(x)(f(x))=x^2+1 ?
The solution to f(x)(f(x))=x^2+1 is Hyperbola with (h,k)=(0,0),a=1,b=1