Solve the equation f (x + 2) = f (x-2) +4, where f (x) = 3 + 2x + x ^ 2

The value of x is -1/2

Solve the equation of f(x + 2) = f(x - 2) + 4, where f(x) = 3 + 2x + x^2

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

f(x + 2) = x^2 + 6x + 11

f(x - 2) = 3 + 2(x - 2) + (x - 2)^2

f(x - 2) = 3 + 2x - 4 + x^2 - 4x + 4

f(x - 2) = x^2 - 2x + 3

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

The value of x is -1/2