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

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

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inverse of f(x)=(1-sqrt(x(1-x)+1))/x

inverse

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

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

Solution steps

y = \frac{1 - x ( 1 - x ) + 1}{x}

Replace

x

with

y

x = \frac{1 - y ( 1 - y ) + 1}{y}

Solve for

y, x = \frac{1 - y ( 1 - y ) + 1}{y}

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

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