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# The function f(x) is defined for 1

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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
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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)

Dec 16, 2017