<h2>
Answer:</h2>
The value of x is -1/2
<h2>
Step-by-step explanation:</h2><h3>Question :</h3>
Solve the equation of f(x + 2) = f(x - 2) + 4, where f(x) = 3 + 2x + x^2
<h3>Solution :</h3>
First, we need to split the equation and find the answer to each function
f(x + 2) = 3 + 2(x + 2) + (x + 2)^2
f(x + 2) = 3 + 2x + 4 + x^2 + 4x + 4
<u>f(x + 2) = x^2 + 6x + 11</u>
f(x - 2) = 3 + 2(x - 2) + (x - 2)^2
f(x - 2) = 3 + 2x - 4 + x^2 - 4x + 4
<u>f(x - 2) = x^2 - 2x + 3</u>
Second, we need to find the value of x
f(x + 2) = f(x - 2) + 4
=> x^2 + 6x + 11 = x^2 - 2x + 3 + 4
=> x^2 - x^2 + 6x + 11 = - 2x + 3 + 4
=> 6x + 11 = -2x + 7
=> 6x = -2x - 4
=> 6x + 2x = -4
=> 8x = -4
=> x = -1/2
<h3>Conclusion :</h3>
The value of x is -1/2
