Use the graph that shows the solution to f(x)=g(x) .

f(x)=1/x−2

g(x)=x−2

What is the solution to f(x)=g(x) ?

Select each correct answer.

−1

1

2

3

would I plug in those vales for x? I am unsure what to do

jjennylove Feb 21, 2019

#3**+2 **

Yep... ...I'd just check the intersection points

On the top graph the points appear to be ( 1 , -1) and (-1, - 3)

So putting x = 1 into both functions results in y = -1

So this is correct

And putting -1 into each function results in y = -3

So....this is also correct

So....we don't even need to check the bottom graph...the top graph has to be the correct one !!!

CPhill Feb 21, 2019

#4**+1 **

The question actually isnt regrading the graphs its asking

What is the solution to f(x)=g(x) ?

Select each correct answer.

−1

1

2

3

it either -1,1,2,or 3 for the answer

jjennylove
Feb 21, 2019

#5**+2 **

OK....I guess they are asking for the x values where the graphs intersect

These are

x = 1 and x = -1

Sorry I missed that !!!

CPhill
Feb 21, 2019

#7**+1 **

well wouldnt we put them to equal? and that would lead to x=3 and x=1 , so the answer would 3 and 1 ?

jjennylove
Feb 21, 2019

#8**+2 **

Jenny....It looks like they just want you to select the x values of their intersections

These would be

-1

1

CPhill
Feb 21, 2019

#10**+2 **

That is kinda' what we did...!!!

If we put x = 1 into 1/x - 2 we get -1

If we put x = 1 into x - 2 we get -1

So ....the same x value plugged into both functions gives the same y value in both functions ....so (1, -1) is an intersection point

Check that x = -1 plugged into both functions gives y = -3

So....the same x value in both functions gives the same y value in both functions....so ( -1 , -3) is the other intersection point

CPhill
Feb 21, 2019

#11**+1 **

oh wait! I see now that makes sense! Im sorry i was thinking something totally different yes that would be the correct way . I am so sorry I was just trying to make sense of it all . Thank you for going over it more with me and answering my questions.

jjennylove
Feb 21, 2019

#12**+2 **

HAHAHA!!!.....this stuff isn't easy.....I hope I make it more understandable

BTW....we could set the functions equal and solve for x

1/x - 2 = x - 2 multiply through by x

1 - 2x = x^2 - 2x simplify

1 = x^2

x^2 = 1 take both roots

x = ±√1

So x = 1 or x = -1

This is sometimes faster than trying to look at a graph!!!

CPhill
Feb 21, 2019

#13**+2 **

You do very well all the time. Your explaintations really help. And oh yes, I am more familair with that then looking at the grah but it is good to know both ways.

jjennylove
Feb 21, 2019