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

The inverse of f(x)=((2x-3))/(4x+5) is (-3-5x)/(2(-1+2x))

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

x^{2} + 2 x - 15

y = \frac{1}{x} + x

(x - 9)^{2} - 6

y = 2 x + 10

(1, 2), (5, 1)

What is the inverse of f(x)=((2x-3))/(4x+5) ?
The inverse of f(x)=((2x-3))/(4x+5) is (-3-5x)/(2(-1+2x))