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Question

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}.