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

The inverse of f(x)= x/2+sqrt((x-2(x+2))/4) is (4x-1+sqrt(-8x-15))/2 ,(4x-1-sqrt(-8x-15))/2

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

inverse

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

\frac{4 x - 1 + - 8 x - 15}{2}, \frac{4 x - 1 - - 8 x - 15}{2}

Solution steps

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

Replace

x

with

y

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

Solve for

y, x = \frac{y}{2} + \frac{y - 2 ( y + 2 )}{4}

\frac{4 x - 1 + - 8 x - 15}{2}, \frac{4 x - 1 - - 8 x - 15}{2}

f (x) = (x + 1)^{0.5}

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

f (x) = - 2 x + 11

f (x) = - 2 x + 12

f (x) = (x - 2)^{3} + 2

What is the inverse of f(x)= x/2+sqrt((x-2(x+2))/4) ?
The inverse of f(x)= x/2+sqrt((x-2(x+2))/4) is (4x-1+sqrt(-8x-15))/2 ,(4x-1-sqrt(-8x-15))/2