+0  
 
+1
197
1
avatar+1442 

The function f(x) is defined for 1

 

         { 2x+1   if 1

f(x)= { 7-x   if 2 < x

         { 10-2x   if 3 < x

        { 10-x   if 4 < x

 

Find all real numbers x such that f(x) = x. 

 

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

 

 

Thanks so much!

AnonymousConfusedGuy  Dec 16, 2017
 #1
avatar+88898 
+3

We want to find all ordered pairs such that  y  = x

 

This cannot happen with the first function whose only ordered pair is (1, 3)

 

With the second function we have that

y  =  7-x       .....so.....

x  = 7 - x       add x to both sides

2x  =  7        divide both sides by 2

x   = 7/2  and this is in the domain of this function...so the ordered pair that make f(x)  = x   for this function is  (7/2, 7/2)

 

 

For the third function, we have that

y  = 10-2x      ......so....

x  = 10-2x        add 2x to both sides

3x  = 10   divide both sides by 3

x  = 10/3   and this is in the domain of this function.....so the ordered pair that make f(x)  = x for this function is (10,3, 10,3)

 

Finally

y  = 10- x     ......so....

x  = 10 - x   add x to both sides

2x  = 10    divide both sides by 2

x  = 5  and this is in the domain  of this function....so the ordered pair that make f(x)  = x  for this function is  (5,5)

 

So.....the ansers are:      (7/2, 7/2), (10/3, 10/ 3) , (5,5)

 

 

 

cool cool cool

CPhill  Dec 16, 2017

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