What is the inverse of f(x)=((3-2x))/(x-5) ?

The inverse of f(x)=((3-2x))/(x-5) is (3+5x)/(x+2)

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inverse of f(x)=((3-2x))/(x-5)

inverse

f (x) = \frac{( 3 - 2 x )}{x - 5}

\frac{3 + 5 x}{x + 2}

Solution steps

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

Replace

x

with

y

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

Solve for

y, x = \frac{3 - 2 y}{y - 5}

\frac{3 + 5 x}{x + 2}

f (x) = \frac{5 x - 3}{\frac{1}{2} - 7 x}

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

\frac{6}{1 + x ^{2}}

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

x^{2} - 5 x - 6

What is the inverse of f(x)=((3-2x))/(x-5) ?
The inverse of f(x)=((3-2x))/(x-5) is (3+5x)/(x+2)