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

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

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inverse of f(x)= 1/2 (x-1)^2

inverse

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

2 x + 1, - 2 x + 1

Solution steps

y = \frac{1}{2} (x - 1)^{2}

Replace

x

with

y

x = \frac{1}{2} (y - 1)^{2}

Solve for

y, x = \frac{1}{2} (y - 1)^{2}

2 x + 1, - 2 x + 1

f (x) = - 2 x + 1 - 3

f (x) = \frac{9 x}{x - 17}

f (x) = \frac{2 x + 5}{5 x + 3}

f (x) = \frac{( 10 - 3 x )}{1 + 2 x}

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