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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, <br /> 7 - x & \text{if }2 < x \le 3, <br /> 10 - 2x &a...Find all real numbers x such that f(x) = x

If you find more than one answer, list them all, separated by commas.

 Jan 8, 2015

Best Answer 

 #1
avatar+95356 
+10

2x+1=x

x=-1     this is NOT in the relevant domain so its no good

 

7-x=x

7=2x

x=3.5   not in given domain

 

10-2x=x

10=3x

x=10/3       YES

 

10-x=x

10=2x

x=5           YES

 

so there are 2 solutions

 

$$x=5\qquad or \qquad x=3\frac{1}{3}$$

 

 pleasse ask if you do not understand :)

 Jan 8, 2015
 #1
avatar+95356 
+10
Best Answer

2x+1=x

x=-1     this is NOT in the relevant domain so its no good

 

7-x=x

7=2x

x=3.5   not in given domain

 

10-2x=x

10=3x

x=10/3       YES

 

10-x=x

10=2x

x=5           YES

 

so there are 2 solutions

 

$$x=5\qquad or \qquad x=3\frac{1}{3}$$

 

 pleasse ask if you do not understand :)

Melody Jan 8, 2015
 #2
avatar+94548 
+5

Very impressive,  Melody...!!!!!

[I tried a WAY more complicated approach....it didn't work as well as this....LOL!!!....genius in simplicity.....!!! ]

 

 Jan 9, 2015
 #3
avatar+95356 
+5

Well it is nice to know that I am capable of choosing a simple method sometimes.

This is very rare for me.    LOL

 Jan 9, 2015
 #4
avatar+94548 
0

LOL!!!!

 

 Jan 9, 2015

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