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

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

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

inverse

f (x) = - 2 x + 4 + 1

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

Solution steps

y = - 2 x + 4 + 1

Replace

x

with

y

x = - 2 y + 4 + 1

Solve for

y, x = - 2 y + 4 + 1

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

\frac{2}{x ^{4} + 4 x ^{2} + 2}

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

f (x) = 4 x^{2} + 12 x + 9

f (x) = x^{2} - 4 x - 4

f (x) = x^{2} - 4 x + 6

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