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

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

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

inverse

f (x) = x + x

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

Solution steps

y = x + x

Replace

x

with

y

x = y + y

Solve for

y, x = y + y

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

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

f (x) = x^{2} + 3 x + 6

\frac{2 x ^{2} - 12 x + 17}{x ^{2} - 8 x + 16}

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

f (x) = - x_{+ 4}

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