What is the inverse of f(x)=((x+3))/((x+6)) ?

The inverse of f(x)=((x+3))/((x+6)) is (3-6x)/(x-1)

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inverse of f(x)=((x+3))/((x+6))

inverse

f (x) = \frac{( x + 3 )}{( x + 6 )}

\frac{3 - 6 x}{x - 1}

Solution steps

y = \frac{x + 3}{x + 6}

Replace

x

with

y

x = \frac{y + 3}{y + 6}

Solve for

y, x = \frac{y + 3}{y + 6}

\frac{3 - 6 x}{x - 1}

f (x) = \frac{x + 8}{x ^{2} + 5 x - 24}

\frac{4 x - 8}{( x - 4 ) ( x + 1 )}

f (x) = 5 x - 12

\frac{2 x ( x - 1 ) ^{2}}{( x + 1 ) ^{3}}

f (x) = \frac{( x + 8 )}{( x - 4 )}

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