What is the inverse of f(x)=2x+sqrt(x+5) ?

The inverse of f(x)=2x+sqrt(x+5) is (4x+1+sqrt(8x+81))/8 ,(4x+1-sqrt(8x+81))/8

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inverse of f(x)=2x+sqrt(x+5)

inverse

f (x) = 2 x + x + 5

\frac{4 x + 1 + 8 x + 81}{8}, \frac{4 x + 1 - 8 x + 81}{8}

Solution steps

y = 2 x + x + 5

Replace

x

with

y

x = 2 y + y + 5

Solve for

y, x = 2 y + y + 5

\frac{4 x + 1 + 8 x + 81}{8}, \frac{4 x + 1 - 8 x + 81}{8}

What is the inverse of f(x)=2x+sqrt(x+5) ?
The inverse of f(x)=2x+sqrt(x+5) is (4x+1+sqrt(8x+81))/8 ,(4x+1-sqrt(8x+81))/8