What is the inverse of f(x)=1-sqrt(4-2x) ?

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

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inverse of f(x)=1-sqrt(4-2x)

inverse

f (x) = 1 - 4 - 2 x

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

Solution steps

y = 1 - 4 - 2 x

Replace

x

with

y

x = 1 - 4 - 2 y

Solve for

y, x = 1 - 4 - 2 y

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

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

arcsec (\frac{1}{x})

f (x) = x - 2, x \geq 2

f (x) = - \frac{3}{2} x + 4

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