What is the inverse of f(x)= 1/x-x ?

The inverse of f(x)= 1/x-x is -(x+sqrt(x^2+4))/2 ,-(x-sqrt(x^2+4))/2

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inverse of f(x)= 1/x-x

inverse

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

- \frac{x + x ^{2} + 4}{2}, - \frac{x - x ^{2} + 4}{2}

Solution steps

y = \frac{1}{x} - x

Replace

x

with

y

x = \frac{1}{y} - y

Solve for

y, x = \frac{1}{y} - y

- \frac{x + x ^{2} + 4}{2}, - \frac{x - x ^{2} + 4}{2}

f (x) = \frac{3 x - 4}{3 - x}

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

f (x) = x^{2} + 8 x + 16

2250 (0.015 - 0.001 x)^{2} + 6000 x

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

What is the inverse of f(x)= 1/x-x ?
The inverse of f(x)= 1/x-x is -(x+sqrt(x^2+4))/2 ,-(x-sqrt(x^2+4))/2