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The function $f(x)$ is defined for $1 \le x \le 5$ as follows: \[f(x) = \left\{ \begin{array}{cl} 2x + 1 & \text{if }1 \le x \le 2, \\ 7 - x & \text{if }2 < x \le 3, \\ 10 - 2x & \text{if }3 < x \le 4, \\ 10 - x & \text{if }4 < x \le 5. \end{array}\right.\] Find all real numbers $x$ such that $f(x) = x$.  If you find more than one answer, list them all, separated by commas.

Guest Aug 28, 2017

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 #1
avatar+18548 
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The function f(x) is defined for \(1 \le x \le 5 \) as follows:
\(\left[f(x) = \left\{ \begin{array}{cl} 2x + 1 & \text{if }1 \le x \le 2, \\ 7 - x & \text{if }2 < x \le 3, \\ 10 - 2x & \text{if }3 < x \le 4, \\ 10 - x & \text{if }4 < x \le 5. \end{array} \right. \right]\)
   

Find all real numbers x such that f(x) = x.  
If you find more than one answer, list them all, separated by commas.

 

 

 

\(x = \{ \frac{10}{3}, 5 \}\)

 

laugh

heureka  Aug 28, 2017
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 #1
avatar+18548 
+2
Best Answer

The function f(x) is defined for \(1 \le x \le 5 \) as follows:
\(\left[f(x) = \left\{ \begin{array}{cl} 2x + 1 & \text{if }1 \le x \le 2, \\ 7 - x & \text{if }2 < x \le 3, \\ 10 - 2x & \text{if }3 < x \le 4, \\ 10 - x & \text{if }4 < x \le 5. \end{array} \right. \right]\)
   

Find all real numbers x such that f(x) = x.  
If you find more than one answer, list them all, separated by commas.

 

 

 

\(x = \{ \frac{10}{3}, 5 \}\)

 

laugh

heureka  Aug 28, 2017

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