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

The inverse of f(x)=x+sqrt(x+2) is (2x+1+sqrt(4x+9))/2 ,(2x+1-sqrt(4x+9))/2

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inverse of f(x)=x+sqrt(x+2)

inverse

f (x) = x + x + 2

\frac{2 x + 1 + 4 x + 9}{2}, \frac{2 x + 1 - 4 x + 9}{2}

Solution steps

y = x + x + 2

Replace

x

with

y

x = y + y + 2

Solve for

y, x = y + y + 2

\frac{2 x + 1 + 4 x + 9}{2}, \frac{2 x + 1 - 4 x + 9}{2}

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

y = \frac{1}{3} x + 4

\frac{x - 7}{2}

f (x) = \frac{8 x}{x + 3}

What is the inverse of f(x)=x+sqrt(x+2) ?
The inverse of f(x)=x+sqrt(x+2) is (2x+1+sqrt(4x+9))/2 ,(2x+1-sqrt(4x+9))/2