What is the inverse of x/(x^2-6x+8) ?

The inverse of x/(x^2-6x+8) is (6x+1+sqrt(4x^2+12x+1))/(2x),(6x+1-sqrt(4x^2+12x+1))/(2x)

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inverse of x/(x^2-6x+8)

inverse

\frac{x}{x ^{2} - 6 x + 8}

\frac{6 x + 1 + 4 x ^{2} + 12 x + 1}{2 x}, \frac{6 x + 1 - 4 x ^{2} + 12 x + 1}{2 x}

Solution steps

y = \frac{x}{x ^{2} - 6 x + 8}

Replace

x

with

y

x = \frac{y}{y ^{2} - 6 y + 8}

Solve for

y, x = \frac{y}{y ^{2} - 6 y + 8}

\frac{6 x + 1 + 4 x ^{2} + 12 x + 1}{2 x}, \frac{6 x + 1 - 4 x ^{2} + 12 x + 1}{2 x}

3 (x - 2)^{2} + 4

f (x) = (4 - x)^{3}

y = x^{2} - 8 x - 6

f (x) = \frac{2 x}{3} - 1

f (x) = - x^{2} + 4

What is the inverse of x/(x^2-6x+8) ?
The inverse of x/(x^2-6x+8) is (6x+1+sqrt(4x^2+12x+1))/(2x),(6x+1-sqrt(4x^2+12x+1))/(2x)