Solve. $f(x)=4x+\frac{17}{x}$

Ledexadvanips
2022-08-04
Answered

Solve. $f(x)=4x+\frac{17}{x}$

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Uriel Whitehead

Answered 2022-08-05
Author has **8** answers

The procedure for finding the inverse is as follows, I will workout the question and explain the procedure at the same time:

$f(x)=4x+\frac{17}{x}$

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 $y={f}^{-1}(x)$

${f}^{-1}(x)=\frac{x}{4{x}^{2}+17}$ This is the inverse.

$f(x)=4x+\frac{17}{x}$

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 $y={f}^{-1}(x)$

${f}^{-1}(x)=\frac{x}{4{x}^{2}+17}$ This is the inverse.

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