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}
g (x) = x + 4, f (x) = 10- x^2 {1, 6}
f (x) = 10 + x^2, g (x) = x + 4 {-3, 1}

Answer 1

The correct choice is the first:

f(x) = 10 − x^2 and g(x) = x + 4.
Solve 10 − x^2 = x + 4 ⇒ −x^2 − x + 6 = 0 ⇒ x^2 + x − 6 = 0 ⇒ (x + 3)(x − 2) = 0.

Solution set: {−3, 2}.