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

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

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inverse of f(x)=((4x))/((9x-1))

inverse

f (x) = \frac{( 4 x )}{( 9 x - 1 )}

\frac{x}{9 x - 4}

Solution steps

y = \frac{4 x}{9 x - 1}

Replace

x

with

y

x = \frac{4 y}{9 y - 1}

Solve for

y, x = \frac{4 y}{9 y - 1}

\frac{x}{9 x - 4}

y = \frac{1}{6} x + \frac{3}{2}

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

f (x) = x^{2} + 10

f (x) = 6 x - 7

y = x^{2} - 2 x

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