What is the inverse of f(x)= 1/(1/x-\frac{1){3x+4}} ?

The inverse of f(x)= 1/(1/x-\frac{1){3x+4}} is (-2+x+sqrt(x^2+8x+4))/3 ,(-2+x-sqrt(x^2+8x+4))/3

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inverse of f(x)= 1/(1/x-\frac{1){3x+4}}

inverse

f (x) = \frac{1}{\frac{1}{x} - \frac{1}{3 x + 4}}

\frac{- 2 + x + x ^{2} + 8 x + 4}{3}, \frac{- 2 + x - x ^{2} + 8 x + 4}{3}

Solution steps

y = \frac{1}{\frac{1}{x} - \frac{1}{3 x + 4}}

Replace

x

with

y

x = \frac{1}{\frac{1}{y} - \frac{1}{3 y + 4}}

Solve for

y, x = \frac{1}{\frac{1}{y} - \frac{1}{3 y + 4}}

\frac{- 2 + x + x ^{2} + 8 x + 4}{3}, \frac{- 2 + x - x ^{2} + 8 x + 4}{3}

What is the inverse of f(x)= 1/(1/x-\frac{1){3x+4}} ?
The inverse of f(x)= 1/(1/x-\frac{1){3x+4}} is (-2+x+sqrt(x^2+8x+4))/3 ,(-2+x-sqrt(x^2+8x+4))/3