What is the inverse of f(x)=((x+1))/((x+2)) ?

The inverse of f(x)=((x+1))/((x+2)) is (1-2x)/(x-1)

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inverse of f(x)=((x+1))/((x+2))

inverse

f (x) = \frac{( x + 1 )}{( x + 2 )}

\frac{1 - 2 x}{x - 1}

Solution steps

y = \frac{x + 1}{x + 2}

Replace

x

with

y

x = \frac{y + 1}{y + 2}

Solve for

y, x = \frac{y + 1}{y + 2}

\frac{1 - 2 x}{x - 1}

\frac{2 x ^{2} + 2 x - 12}{x ^{2} + x}

- x^{2} + x - 5

\frac{( x + 1 )}{2 x + 1}

\frac{8}{x + 4}

f (x) = \frac{( \frac{5}{x} )}{( \frac{5}{x} ) + 5}

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