What is the inverse of (sqrt(x+1))/x ?

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

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inverse of (sqrt(x+1))/x

inverse

\frac{x + 1}{x}

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

Solution steps

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

Replace

x

with

y

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

Solve for

y, x = \frac{y + 1}{y}

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

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