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

The inverse of f(x)=2-x+sqrt(1-2x) is (-2x+2+sqrt(8x-8))/2 ,(-2x+2-sqrt(8x-8))/2

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

inverse

f (x) = 2 - x + 1 - 2 x

\frac{- 2 x + 2 + 8 x - 8}{2}, \frac{- 2 x + 2 - 8 x - 8}{2}

Solution steps

y = 2 - x + 1 - 2 x

Replace

x

with

y

x = 2 - y + 1 - 2 y

Solve for

y, x = 2 - y + 1 - 2 y

\frac{- 2 x + 2 + 8 x - 8}{2}, \frac{- 2 x + 2 - 8 x - 8}{2}

What is the inverse of f(x)=2-x+sqrt(1-2x) ?
The inverse of f(x)=2-x+sqrt(1-2x) is (-2x+2+sqrt(8x-8))/2 ,(-2x+2-sqrt(8x-8))/2