What is f(x)(x)^{-1}f(x)=5x-3 ?

The solution to f(x)(x)^{-1}f(x)=5x-3 is Hyperbola with (h,k)=(3/10 ,0),a= 3/10 ,b= 3/(2sqrt(5))

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f(x)(x)^{-1}f(x)=5x-3

f (x) (x)^{- 1} f (x) = 5 x - 3

(h, k) = (\frac{3}{10}, 0), a = \frac{3}{10}, b = \frac{3}{2 5}

Solution steps

y x^{- 1} y = 5 x - 3

Rewrite

y x^{- 1} y - 5 x + 3 = 0

in the form of a standard hyperbola equation

\frac{( x - \frac{3}{10} ) ^{2}}{( \frac{3}{10} ) ^{2}} - \frac{( y - 0 ) ^{2}}{( \frac{3}{2 5} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{3}{10}, 0), a = \frac{3}{10}, b = \frac{3}{2 5}

x^{2} + 3 x - 2 y^{2} + 4 y = 2

4 x^{2} + 16 x - 25 y^{2} + 50 y - 109 = 0

\frac{y ^{2}}{36} - \frac{x ^{2}}{14} = 1

\frac{( x - 2 ) ^{2}}{4} - (y - 1)^{2} = 1

\frac{x ^{2}}{16} - \frac{y ^{2}}{20} = 1

What is f(x)(x)^{-1}f(x)=5x-3 ?
The solution to f(x)(x)^{-1}f(x)=5x-3 is Hyperbola with (h,k)=(3/10 ,0),a= 3/10 ,b= 3/(2sqrt(5))