What is the inverse of f(x)=(x^2-2)/x ?

The inverse of f(x)=(x^2-2)/x is (x+sqrt(x^2+8))/2 ,(x-sqrt(x^2+8))/2

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inverse of f(x)=(x^2-2)/x

inverse

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

\frac{x + x ^{2} + 8}{2}, \frac{x - x ^{2} + 8}{2}

Solution steps

y = \frac{x ^{2} - 2}{x}

Replace

x

with

y

x = \frac{y ^{2} - 2}{y}

Solve for

y, x = \frac{y ^{2} - 2}{y}

\frac{x + x ^{2} + 8}{2}, \frac{x - x ^{2} + 8}{2}

f (x) = \frac{( 2 x + 5 )}{x - 7}

f (x) = 2^{2 x}

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

f (x) = \frac{3 x + 8}{5}

f (x) = \frac{1}{5} x - 7

What is the inverse of f(x)=(x^2-2)/x ?
The inverse of f(x)=(x^2-2)/x is (x+sqrt(x^2+8))/2 ,(x-sqrt(x^2+8))/2