What is the inverse of f(x)=((x+2))/((x+5)) ?

The inverse of f(x)=((x+2))/((x+5)) is (2-5x)/(x-1)

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inverse of f(x)=((x+2))/((x+5))

inverse

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

\frac{2 - 5 x}{x - 1}

Solution steps

y = \frac{x + 2}{x + 5}

Replace

x

with

y

x = \frac{y + 2}{y + 5}

Solve for

y, x = \frac{y + 2}{y + 5}

\frac{2 - 5 x}{x - 1}

y = \frac{1}{x}

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

y = \frac{5 x ^{2} - 3}{x + 2}

f (x) = x e^{2 x}

\frac{1}{5}

What is the inverse of f(x)=((x+2))/((x+5)) ?
The inverse of f(x)=((x+2))/((x+5)) is (2-5x)/(x-1)