What is the inverse of (x+5)/(x^2-3x+5) ?

The inverse of (x+5)/(x^2-3x+5) is (3x+1+sqrt(-11x^2+26x+1))/(2x),(3x+1-sqrt(-11x^2+26x+1))/(2x)

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inverse of (x+5)/(x^2-3x+5)

inverse

\frac{x + 5}{x ^{2} - 3 x + 5}

\frac{3 x + 1 + - 11 x ^{2} + 26 x + 1}{2 x}, \frac{3 x + 1 - - 11 x ^{2} + 26 x + 1}{2 x}

Solution steps

y = \frac{x + 5}{x ^{2} - 3 x + 5}

Replace

x

with

y

x = \frac{y + 5}{y ^{2} - 3 y + 5}

Solve for

y, x = \frac{y + 5}{y ^{2} - 3 y + 5}

\frac{3 x + 1 + - 11 x ^{2} + 26 x + 1}{2 x}, \frac{3 x + 1 - - 11 x ^{2} + 26 x + 1}{2 x}

f (x) = 2 ln (\frac{( x + 3 )}{5})

f (x) = - \frac{9}{8 x}

\frac{1}{x} + 1

f (x) = 4 (x - 1)^{3} + 2

f (x) = ln (3 x - 5) - ln (x + 9) + 5, x = 5

What is the inverse of (x+5)/(x^2-3x+5) ?
The inverse of (x+5)/(x^2-3x+5) is (3x+1+sqrt(-11x^2+26x+1))/(2x),(3x+1-sqrt(-11x^2+26x+1))/(2x)