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Question
To show how to solve the equation, create two functions and find an intersection point. What two functions can be used to solve the following equation, and what is a solution set?

10−x2=x+4


(1 point)
Responses

f(x)=10−x2, g(x)=x+4, {−3, 1}
f(x)=10−x2, g(x)=x+4, {−3, 1}

f(x)=10+x2, g(x)=x−4, {−3, 1}
f(x)=10+x2, g(x)=x−4, {−3, 1}

g(x)=x+4, f(x)=10−x2, {1, 6}
g(x)=x+4, f(x)=10−x2, {1, 6}

g(x)=x+4, f(x)=10+x2, {−3, 2}

Answer 1

To solve the equation \(10 - x^2 = x + 4\), we can create two functions based on the left and right sides of the equation.

1. **Function 1 (f)**: \(f(x) = 10 - x^2\)
2. **Function 2 (g)**: \(g(x) = x + 4\)

Now, we need to find the intersection points of these two functions, which will give us the solutions to the original equation. This means we want to find \(x\) values where \(f(x) = g(x)\):

\[
10 - x^2 = x + 4
\]

Rearranging this equation gives:

\[
-x^2 - x + 6 = 0
\]

Multiplying through by -1, we have:

\[
x^2 + x - 6 = 0
\]

Now, we can factor this quadratic:

\[
(x - 2)(x + 3) = 0
\]

Setting each factor to zero gives us the solutions:

\[
x - 2 = 0 \quad \Rightarrow \quad x = 2
\]
\[
x + 3 = 0 \quad \Rightarrow \quad x = -3
\]

So, the solution set is \(\{-3, 2\}\).

Therefore, the correct response is:
**f(x)=10−x², g(x)=x+4, {−3, 2}**.