Question
To show how to solve the equation, create two functions and find their intersection points. What two functions can be used to solve the following equation, and what is their solution set?
x²+4x-1=2x+2
• f(x)= x²+4x-1,g(x)=2x+2, {-3,1}
• f(x)= x²+4x-1,g(x)=2x+2, {-3,-4,1,4}
• f(x)=x²+4x, g(x)= 2x, {-3,1}
• f(x)=x²+4x-1,g(x)=2x+2, {-1,3}
x²+4x-1=2x+2
• f(x)= x²+4x-1,g(x)=2x+2, {-3,1}
• f(x)= x²+4x-1,g(x)=2x+2, {-3,-4,1,4}
• f(x)=x²+4x, g(x)= 2x, {-3,1}
• f(x)=x²+4x-1,g(x)=2x+2, {-1,3}
Answers
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Answered by
GPT 3.5
The correct functions to use to solve the equation x²+4x-1=2x+2 are f(x) = x²+4x-1 and g(x) = 2x+2.
To solve for the intersection points of these functions, set them equal to each other:
x²+4x-1 = 2x+2
Rearranging the equation gives:
x²+2x-3 = 0
Now, factor the quadratic equation:
(x+3)(x-1) = 0
Set each factor equal to zero to find the values of x:
x+3 = 0
x = -3
x-1 = 0
x = 1
Therefore, the solution set for the equation x²+4x-1=2x+2 is {-3, 1}. So, f(x) = x²+4x-1 and g(x) = 2x+2 have intersection points at x = -3 and x = 1.
To solve for the intersection points of these functions, set them equal to each other:
x²+4x-1 = 2x+2
Rearranging the equation gives:
x²+2x-3 = 0
Now, factor the quadratic equation:
(x+3)(x-1) = 0
Set each factor equal to zero to find the values of x:
x+3 = 0
x = -3
x-1 = 0
x = 1
Therefore, the solution set for the equation x²+4x-1=2x+2 is {-3, 1}. So, f(x) = x²+4x-1 and g(x) = 2x+2 have intersection points at x = -3 and x = 1.
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