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

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

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

inverse

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

- \frac{4 x ^{2} - 4 x - 3}{4}

Solution steps

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

Replace

x

with

y

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

Solve for

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

- \frac{4 x ^{2} - 4 x - 3}{4}

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