What is the inverse of f(x)=((x+6))/((x-5)) ?

The inverse of f(x)=((x+6))/((x-5)) is (6+5x)/(x-1)

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inverse of f(x)=((x+6))/((x-5))

inverse

f (x) = \frac{( x + 6 )}{( x - 5 )}

\frac{6 + 5 x}{x - 1}

Solution steps

y = \frac{x + 6}{x - 5}

Replace

x

with

y

x = \frac{y + 6}{y - 5}

Solve for

y, x = \frac{y + 6}{y - 5}

\frac{6 + 5 x}{x - 1}

y = \frac{1}{10} x^{2} - 4 x + 9

f (x) = 4 x^{2} - x - 3

y = 2 x + 5

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

y = 5 x + 4

What is the inverse of f(x)=((x+6))/((x-5)) ?
The inverse of f(x)=((x+6))/((x-5)) is (6+5x)/(x-1)