What is the inverse of f(x)=4x+1/x ?

The inverse of f(x)=4x+1/x is (x+sqrt(x^2-16))/8 ,(x-sqrt(x^2-16))/8

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inverse of f(x)=4x+1/x

inverse

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

\frac{x + x ^{2} - 16}{8}, \frac{x - x ^{2} - 16}{8}

Solution steps

y = 4 x + \frac{1}{x}

Replace

x

with

y

x = 4 y + \frac{1}{y}

Solve for

y, x = 4 y + \frac{1}{y}

\frac{x + x ^{2} - 16}{8}, \frac{x - x ^{2} - 16}{8}

What is the inverse of f(x)=4x+1/x ?
The inverse of f(x)=4x+1/x is (x+sqrt(x^2-16))/8 ,(x-sqrt(x^2-16))/8