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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−x^2=x+4

(1 point)
Responses

g(x)=x+4
, f(x)=10+x2
, {−3, 2}
g of x is equal to x plus 4, f of x is equal to 10 plus x squared, {−3, 2}

f(x)=10−x2
, g(x)=x+4
, {−3, 2}
f of x is equal to 10 minus x squared, g of x is equal to x plus 4, {−3, 2}

g(x)=x+4
, f(x)=10−x2
, {1, 6}
g of x is equal to x plus 4, f of x is equal to 10 minus x squared, {1, 6}

f(x)=10+x2
, g(x)=x+4
, {−3, 1}

1 answer

To solve the equation \(10 - x^2 = x + 4\), we can create two functions that represent the two sides of the equation:

  1. \(f(x) = 10 - x^2\) (this represents the left side of the equation)
  2. \(g(x) = x + 4\) (this represents the right side of the equation)

The next step is to find the intersection points of these two functions, which means we need to solve the equation:

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

Rearranging this equation gives:

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

which simplifies to:

\[ 6 = x + x^2 \]

or

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

Now, we will solve this quadratic equation using factoring:

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

Setting each factor equal to zero gives us:

  1. \(x - 2 = 0 \Rightarrow x = 2\)
  2. \(x + 3 = 0 \Rightarrow x = -3\)

Therefore, the solution set is:

\({ -3, 2 }\)

Putting this together, we have:

  • \(f(x) = 10 - x^2\)
  • \(g(x) = x + 4\)
  • The solution set is \({ -3, 2 }\).

So the correct option is:

f(x)=10−x^2, g(x)=x+4, {−3, 2}.