What is the inverse of f(x)=(4x+3)/(9+4x) ?

The inverse of f(x)=(4x+3)/(9+4x) is (3-9x)/(4(-1+x))

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inverse of f(x)=(4x+3)/(9+4x)

inverse

f (x) = \frac{4 x + 3}{9 + 4 x}

\frac{3 - 9 x}{4 ( - 1 + x )}

Solution steps

y = \frac{4 x + 3}{9 + 4 x}

Replace

x

with

y

x = \frac{4 y + 3}{9 + 4 y}

Solve for

y, x = \frac{4 y + 3}{9 + 4 y}

\frac{3 - 9 x}{4 ( - 1 + x )}

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

f (x) = \frac{- 12}{x ^{2} + 8 x + 12}

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

4 x + 10 y = - 20

6 - 7 x

What is the inverse of f(x)=(4x+3)/(9+4x) ?
The inverse of f(x)=(4x+3)/(9+4x) is (3-9x)/(4(-1+x))