What is the inverse of f(x)=(5x-2)/(4-5x) ?

The inverse of f(x)=(5x-2)/(4-5x) is -(-2-4x)/(5(1+x))

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inverse of f(x)=(5x-2)/(4-5x)

inverse

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

- \frac{- 2 - 4 x}{5 ( 1 + x )}

Solution steps

y = \frac{5 x - 2}{4 - 5 x}

Replace

x

with

y

x = \frac{5 y - 2}{4 - 5 y}

Solve for

y, x = \frac{5 y - 2}{4 - 5 y}

- \frac{- 2 - 4 x}{5 ( 1 + x )}

f (x) = \frac{x}{9 + x ^{2}}

f (x) = 4 - 7 x

f (x) = - 6 x + 8

f (x) = 4 - 4 \frac{3 x + 2}{15}

f (x) = - x - 7

What is the inverse of f(x)=(5x-2)/(4-5x) ?
The inverse of f(x)=(5x-2)/(4-5x) is -(-2-4x)/(5(1+x))