What is the inverse of f(x)=x+2/(x-3) ?

The inverse of f(x)=x+2/(x-3) is (3+x+sqrt(x^2-6x+1))/2 ,(3+x-sqrt(x^2-6x+1))/2

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inverse of f(x)=x+2/(x-3)

inverse

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

\frac{3 + x + x ^{2} - 6 x + 1}{2}, \frac{3 + x - x ^{2} - 6 x + 1}{2}

Solution steps

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

Replace

x

with

y

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

Solve for

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

\frac{3 + x + x ^{2} - 6 x + 1}{2}, \frac{3 + x - x ^{2} - 6 x + 1}{2}

f (x) = e^{2 x} + 4 e^{x} - 5

f (x) = \frac{2 x}{x - 7}

f (y) = x^{2}

5 x^{4} + 3

\frac{3 x - 5}{2}

What is the inverse of f(x)=x+2/(x-3) ?
The inverse of f(x)=x+2/(x-3) is (3+x+sqrt(x^2-6x+1))/2 ,(3+x-sqrt(x^2-6x+1))/2