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What are the coordinates of the points where the graphs of f(x)=x^3-x^2+x+1 and g(x)=x^3+x^2+x-1intersect? Give your answer as a list of points separated by semicolons. (So "(1,-3); (2,3); (5,-7)" is a valid answer format.)

 Nov 16, 2014

Best Answer 

 #4
avatar+130511 
+5

Eh.....you're not "stupid".....you just need a little help.....!!!

Here we go....

Putting "1" into g(x), we have

(1)^3 + (1)^2 + (1) - 1  =  1 + 1 + 1 - 1 =  2

Putting "-1" into g(x) we have

(-1)^3 + (-1)^2 + (-1) - 1 = -1 + 1 - 1 - 1  = -2

So...the points of intersection are (1, 2) and (-1, -2)

Not too bad, huh???

 

 Nov 16, 2014
 #1
avatar+33661 
+5

x3 - x2 + x +1 = x3 + x2 +x -1 

 

 - x2 + 1 =  x2 -1 

 

x2 = 1

 

x = ±1

 

You can take it from here

.

 Nov 16, 2014
 #2
avatar
0

I am very stupid and don't know what to do next. SO sorry

 Nov 16, 2014
 #3
avatar+33661 
+5

Insert the values of x into either f(x) or g(x) and work out the values.

 

The points will be (1, f(1)); (-1, f(-1))

.

 Nov 16, 2014
 #4
avatar+130511 
+5
Best Answer

Eh.....you're not "stupid".....you just need a little help.....!!!

Here we go....

Putting "1" into g(x), we have

(1)^3 + (1)^2 + (1) - 1  =  1 + 1 + 1 - 1 =  2

Putting "-1" into g(x) we have

(-1)^3 + (-1)^2 + (-1) - 1 = -1 + 1 - 1 - 1  = -2

So...the points of intersection are (1, 2) and (-1, -2)

Not too bad, huh???

 

CPhill Nov 16, 2014

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