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

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

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

inverse

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

\frac{- 9 + 4 x}{x - 4}

Solution steps

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

Replace

x

with

y

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

Solve for

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

\frac{- 9 + 4 x}{x - 4}

3 x - 4

\frac{1}{x} + 1

f (x) = x - 4 y - 11 = 0

y = \frac{x ^{2} + 4 x}{x + 4}

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

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