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

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

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

inverse

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

- \frac{5 - 2 x}{4 + 5 x}

Solution steps

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

Replace

x

with

y

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

Solve for

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

- \frac{5 - 2 x}{4 + 5 x}

\frac{1}{2 x + 4}

f (x) = (\frac{x - 2}{7})^{\frac{1}{3}}

f (x) = 36 x + \frac{9}{x}

f (x) = \frac{1}{x ^{2} - x - 90}

f (x) = \frac{( x - 1 )}{( x + 2 )}

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