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

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

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College
Calculus and Analysis
Differential Calculus
Inverse Functions

Ledexadvanips

Answered question

2022-08-04

Solve.

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

Answer & Explanation

Uriel Whitehead

Beginner2022-08-05Added 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) = 4 x + \frac{17}{x}

First step: change f(x) to y

y = 4 x + \frac{17}{x}

Second step: swap x and y

x = 4 y + \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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