What is the inverse of f(x)=((x^{(2)}-2))/((2x+1)) ?

The inverse of f(x)=((x^{(2)}-2))/((2x+1)) is x+sqrt(x^2+x+2),x-sqrt(x^2+x+2)

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inverse of f(x)=((x^{(2)}-2))/((2x+1))

inverse

f (x) = \frac{( x ^{(2)} - 2 )}{( 2 x + 1 )}

x + x^{2} + x + 2, x - x^{2} + x + 2

Solution steps

y = \frac{x ^{2} - 2}{2 x + 1}

Replace

x

with

y

x = \frac{y ^{2} - 2}{2 y + 1}

Solve for

y, x = \frac{y ^{2} - 2}{2 y + 1}

x + x^{2} + x + 2, x - x^{2} + x + 2

\frac{x}{6} + 8

f (x) = \frac{x - 6}{6 x + 12}

f (x) = 3 ln (5 x - 2) + 6

\frac{x}{6} + 2

f (x) = 5^{x - 1} - 2

What is the inverse of f(x)=((x^{(2)}-2))/((2x+1)) ?
The inverse of f(x)=((x^{(2)}-2))/((2x+1)) is x+sqrt(x^2+x+2),x-sqrt(x^2+x+2)