What is the inverse of f(x)=((10+4x))/(5x+6) ?

The inverse of f(x)=((10+4x))/(5x+6) is (10-6x)/(5x-4)

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inverse of f(x)=((10+4x))/(5x+6)

inverse

f (x) = \frac{( 10 + 4 x )}{5 x + 6}

\frac{10 - 6 x}{5 x - 4}

Solution steps

y = \frac{10 + 4 x}{5 x + 6}

Replace

x

with

y

x = \frac{10 + 4 y}{5 y + 6}

Solve for

y, x = \frac{10 + 4 y}{5 y + 6}

\frac{10 - 6 x}{5 x - 4}

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

\frac{7 x ( 3 x ^{2} - 12 x + 5 )}{3 x ^{2}}

y = 6 x - 11

f (x) = 5 - 3 x^{2} x - 3

f (x) = (x)^{- 1} = \frac{3 x - 4}{2 - x}

What is the inverse of f(x)=((10+4x))/(5x+6) ?
The inverse of f(x)=((10+4x))/(5x+6) is (10-6x)/(5x-4)