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**+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)

CPhill
Dec 16, 2017