Forum
Forums
Questions and Answe...
Algebra
Formulas
Functions and equat...
 
Share:
Notifications
Clear all

[Solved] Functions and equations together

 
Formulas
Last Post by Staff 4 years ago
1 Posts
1 Users
0 Reactions
505 Views
RSS
0
June 15, 2021 12:13 pm
Topic starter
Staff 
(@armor)
Admin
  Honorable Member
317 Posts
156 153 0

Given     f(x)=x-\frac{1}{x},   solve the equation f[f(x)]=x.

 

Add a comment
1 Answer
0
June 15, 2021 12:14 pm
Topic starter
Staff 
(@armor)
Admin
  Honorable Member
317 Posts
156 153 0

\small f[f(x)]=x-\frac{1}{x}-\frac{1}{x-\frac{1}{x}}=\frac{x^4-3x^2+1}{x^3-x},

thus  \small f[f(x)]=x\Leftrightarrow \frac{x^4-3x^2+1}{x^3-x}=x

\small \Rightarrow x^2=\frac{1}{2}\Rightarrow x=\pm \frac{\sqrt{2}}{2}.

Add a comment
Forum Jump:
  Previous Topic
Next Topic  
Share: