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# f(x) to g(x)

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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) ?

−1

1

2

3

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

Feb 21, 2019
edited by jjennylove  Feb 21, 2019

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if so , wouldnt it then be -1 and 1 for the 2 answers?

Feb 21, 2019
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im not to sure

jjennylove  Feb 21, 2019
edited by jjennylove  Feb 21, 2019
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You were correct!!!!

CPhill  Feb 21, 2019
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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 !!!

Feb 21, 2019
#4
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What is the solution to f(x)=g(x) ?

−1

1

2

3

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

jjennylove  Feb 21, 2019
edited by jjennylove  Feb 21, 2019
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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
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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
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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
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i think we would need to use the intersection points to solve f(x)=g(x)

jjennylove  Feb 21, 2019
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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
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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
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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
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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