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?
10-x²=x+4
• f(x)=10-x² , g(x)=x+4 {-3,2}
• g(x)=x+4 , f(x)=10+x², {-3,2}
• f(x)=10+x² , g(x)=x+4{-3,1}
• g(x)=x+4f(x)= 10-x², {1,6}
The correct functions to use to solve the equation 10-x²=x+4 are:
f(x) = 10 - x²
g(x) = x + 4
To find the intersection points of these two functions, set them equal to each other and solve for x:
10 - x² = x + 4
0 = x² + x - 6
0 = (x + 3)(x - 2)
Setting each factor equal to zero, we get:
x + 3 = 0 --> x = -3
x - 2 = 0 --> x = 2
Therefore, the solution set for the equation 10-x²=x+4 is {-3, 2}.