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

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

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

inverse

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

- \frac{1 - 2 x}{5 + x}

Solution steps

y = \frac{5 x + 1}{2 - x}

Replace

x

with

y

x = \frac{5 y + 1}{2 - y}

Solve for

y, x = \frac{5 y + 1}{2 - y}

- \frac{1 - 2 x}{5 + x}

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

f (x) = \frac{1}{x ^{2} - \frac{1}{9}}

5 x^{3} + 9

x^{5} + 1

x^{5} + 7

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