What is the inverse of f(x)=(4x+5)/(2x-3) ?

The inverse of f(x)=(4x+5)/(2x-3) is (5+3x)/(2(-2+x))

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inverse of f(x)=(4x+5)/(2x-3)

inverse

f (x) = \frac{4 x + 5}{2 x - 3}

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

Solution steps

y = \frac{4 x + 5}{2 x - 3}

Replace

x

with

y

x = \frac{4 y + 5}{2 y - 3}

Solve for

y, x = \frac{4 y + 5}{2 y - 3}

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

y = \frac{x}{2}

f (x) = \frac{x ^{\frac{1}{3}} + 2}{x ^{\frac{1}{3}} - 2}

2^{- x}

f (x) = - 2 x - 6

f (x) = 5 x^{\frac{1}{5}}

What is the inverse of f(x)=(4x+5)/(2x-3) ?
The inverse of f(x)=(4x+5)/(2x-3) is (5+3x)/(2(-2+x))