What is the inverse of f(x)=(x-1)/(x+5),x\ne-5 ?

The inverse of f(x)=(x-1)/(x+5),x\ne-5 is (-1-5x)/(x-1)

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inverse of f(x)=(x-1)/(x+5),x\ne-5

inverse

f (x) = \frac{x - 1}{x + 5}, x \neq = - 5

\frac{- 1 - 5 x}{x - 1}

Solution steps

y = \frac{x - 1}{x + 5}

Replace

x

with

y

x = \frac{y - 1}{y + 5}

Solve for

y, x = \frac{y - 1}{y + 5}

\frac{- 1 - 5 x}{x - 1}

What is the inverse of f(x)=(x-1)/(x+5),x\ne-5 ?
The inverse of f(x)=(x-1)/(x+5),x\ne-5 is (-1-5x)/(x-1)