# Solve. f(x)=4x+ 17/x

Solve. $f\left(x\right)=4x+\frac{17}{x}$
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The procedure for finding the inverse is as follows, I will workout the question and explain the procedure at the same time:
$f\left(x\right)=4x+\frac{17}{x}$
First step: change f(x) to y
$y=4x+\frac{17}{x}$
Second step: swap x and y
$x=4y+\frac{17}{y}$
Third step: Re-solve for y
After further solving, we find that $y=\frac{x}{4{x}^{2}+17}$
Fourth step: replace y with $y={f}^{-1}\left(x\right)$
${f}^{-1}\left(x\right)=\frac{x}{4{x}^{2}+17}$ This is the inverse.