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?

Question

x2+4x−1=2x+2


(1 point)
Responses

f(x)=x2+4x
, g(x)=2x
, {−3,1}
f left parenthesis x right parenthesis equals x squared plus 4 x , g left parenthesis x right parenthesis equals 2 x , left brace negative 3 comma 1 right brace

f(x)=x2+4x−1
, g(x)=2x+2
, {−3,−4,1,4}
f left parenthesis x right parenthesis equals x squared plus 4 x minus 1 , g left parenthesis x right parenthesis equals 2 x plus 2 , left brace negative 3 comma negative 4 comma 1 comma 4 right brace

f(x)=x2+4x−1
, g(x)=2x+2
, {−3,1}
f left parenthesis x right parenthesis equals x squared plus 4 x minus 1 , g left parenthesis x right parenthesis equals 2 x plus 2 , left brace negative 3 comma 1 right brace

f(x)=x2+4x−1
, g(x)=2x+2
, {−1,3}

Answer 1

To solve the equation \( x^2 + 4x - 1 = 2x + 2 \), we can rearrange it into the form \( f(x) = g(x) \) by bringing all terms to one side. Here’s how we can define two functions:

Let's define:

• \( f(x) = x^2 + 4x - 1 \)
• \( g(x) = 2x + 2 \)

Now, we need to find the intersection points of these two functions, which are the solutions to the equation \( x^2 + 4x - 1 = 2x + 2 \).

Substituting \( g(x) \) into the equation:

\[ x^2 + 4x - 1 = 2x + 2 \]

Rearranging gives:

\[ x^2 + 4x - 2x - 1 - 2 = 0 \]

\[ x^2 + 2x - 3 = 0 \]

Now, we can factor the quadratic:

\[ (x + 3)(x - 1) = 0 \]

Setting each factor to zero gives us the solutions:

\[ x + 3 = 0 \quad \Rightarrow \quad x = -3 \] \[ x - 1 = 0 \quad \Rightarrow \quad x = 1 \]

Thus, the solution set is \( {-3, 1} \).

So, the correct pair of functions and their solution set is:

\( f(x) = x^2 + 4x - 1 \) and \( g(x) = 2x + 2 \), with the solution set \( {-3, 1} \).