Finding the Inverse of f(x) = x/(x+4)

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SUMMARY

The discussion focuses on finding the inverse of the function f(x) = x/(x+4). The user initially replaces f(x) with y and attempts to isolate x, leading to the equation xy + 4y = x. After some manipulation, the correct approach is revealed, resulting in the inverse function x = -4y/(y-1). This method emphasizes the importance of rearranging equations properly to isolate the variable of interest.

PREREQUISITES
  • Understanding of function notation and inverse functions
  • Algebraic manipulation skills, including solving for variables
  • Familiarity with the concept of isolating variables in equations
  • Basic knowledge of rational functions
NEXT STEPS
  • Study the process of finding inverses of rational functions
  • Learn about algebraic techniques for isolating variables in equations
  • Explore the implications of function inverses in calculus
  • Practice with additional examples of finding inverses for various types of functions
USEFUL FOR

Students studying algebra, mathematics educators, and anyone interested in mastering the concept of function inverses and algebraic manipulation techniques.

RidiculousName
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Hello, I am trying to find the inverse of f(x) = x $$ \div$$ (x+4)

IIRC i need to replace f(x) with y and solve for x.

I've tried to do y = x $$\div$$ (x+4) becomes y(x+4) = x then xy + 4y = x but I can't reduce the amount of x to one.

What am I doing wrong in this problem?
 
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RidiculousName said:
Hello, I am trying to find the inverse of f(x) = x $$ \div$$ (x+4)

IIRC i need to replace f(x) with y and solve for x.

I've tried to do y = x $$\div$$ (x+4) becomes y(x+4) = x then xy + 4y = x but I can't reduce the amount of x to one.

What am I doing wrong in this problem?

Hi Mr. Ridiculous, welcome to MHB! ;)

We can take it a couple of steps further:

xy + 4y = x
xy - x + 4y = 0
xy - x = -4y
x(y - 1) = -4y
x = -4y $$\div$$ (y-1)
 
Thanks! I forgot I could leave the right side of the equation as zero.
 

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