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

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

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

inverse

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

\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 )}

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