What is the inverse of f(x)=((x+7))/(x-5) ?

The inverse of f(x)=((x+7))/(x-5) is (7+5x)/(x-1)

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inverse of f(x)=((x+7))/(x-5)

inverse

f (x) = \frac{( x + 7 )}{x - 5}

\frac{7 + 5 x}{x - 1}

Solution steps

y = \frac{x + 7}{x - 5}

Replace

x

with

y

x = \frac{y + 7}{y - 5}

Solve for

y, x = \frac{y + 7}{y - 5}

\frac{7 + 5 x}{x - 1}

y = x

f (x) = 2 x^{3} - 9 x^{2} + 27

f (x) = - x^{2} + 6 x - 5

y = 5 x

f (x) = \frac{2 x + 3}{6}

What is the inverse of f(x)=((x+7))/(x-5) ?
The inverse of f(x)=((x+7))/(x-5) is (7+5x)/(x-1)