What is the inverse of f(x)=(2/3-8/3 x)/(2/3 x-8/3) ?

The inverse of f(x)=(2/3-8/3 x)/(2/3 x-8/3) is (1+4x)/(x+4)

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inverse of f(x)=(2/3-8/3 x)/(2/3 x-8/3)

inverse

f (x) = \frac{\frac{2}{3} - \frac{8}{3} x}{\frac{2}{3} x - \frac{8}{3}}

\frac{1 + 4 x}{x + 4}

Solution steps

y = \frac{\frac{2}{3} - \frac{8}{3} x}{\frac{2}{3} x - \frac{8}{3}}

Replace

x

with

y

x = \frac{\frac{2}{3} - \frac{8}{3} y}{\frac{2}{3} y - \frac{8}{3}}

Solve for

y, x = \frac{\frac{2}{3} - \frac{8}{3} y}{\frac{2}{3} y - \frac{8}{3}}

\frac{1 + 4 x}{x + 4}

- \frac{x - 2}{4}

y = 5 x + 3

f (x) = \frac{5 8 \cdot x ^{2}}{2}

f (x) = (t - 1) (7 t + 6)

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What is the inverse of f(x)=(2/3-8/3 x)/(2/3 x-8/3) ?
The inverse of f(x)=(2/3-8/3 x)/(2/3 x-8/3) is (1+4x)/(x+4)