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) = (x - 3)^{2} - 8, x > 3

- 7 x - 4

- 3 - 2 x + 3

arctan (4 x)

f (x) = 8 x^{3} + 3

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