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

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

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inverse of f(x)= x/2+sqrt((x^2)/4-1)

inverse

f (x) = \frac{x}{2} + \frac{x ^{2}}{4} - 1

\frac{x ^{2} + 1}{x}

Solution steps

y = \frac{x}{2} + \frac{x ^{2}}{4} - 1

Replace

x

with

y

x = \frac{y}{2} + \frac{y ^{2}}{4} - 1

Solve for

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

\frac{x ^{2} + 1}{x}

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