We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
+1
315
1
avatar+1432 

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!

 Dec 16, 2017
 #1
avatar+99276 
+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

 Dec 16, 2017

24 Online Users

avatar
avatar
avatar
avatar