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

The inverse of f(x)=(5+3x)/(2-3x) is -(5-2x)/(3(1+x))

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

inverse

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

- \frac{5 - 2 x}{3 ( 1 + x )}

Solution steps

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

Replace

x

with

y

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

Solve for

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

- \frac{5 - 2 x}{3 ( 1 + x )}

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

f (x) = \frac{12 x ^{2}}{x ^{4} + 36}

f (x) = (x - 4)

x - 6

What is the inverse of f(x)=(5+3x)/(2-3x) ?
The inverse of f(x)=(5+3x)/(2-3x) is -(5-2x)/(3(1+x))