Question

To show how to solve the equation, create two functions and then find their intersection points. What two functions can be used to solve the following equation, and what is their solution set?

10 - x^2 = x + 4

f (x) = 10 - x^2, g (x) = x + 4 {-3, 2}
g (x) = x - 4, f (x) = 10 + x^2 {-3, 2}

Answer 1

Use the two functions
f(x) = 10 − x^2 and g(x) = x + 4.
Their intersections satisfy 10 − x^2 = x + 4. Rearranging gives
x^2 + x − 6 = 0 = (x + 3)(x − 2),
so x = −3 or x = 2. Thus the solution set (x-values) is {−3, 2}.

(The intersection points are (−3, 1) and (2, 6).)