Final answer:
To find the equal values of x for f(x) and g(x), set x^2 + 2x + 1 equal to 3x + 3 to form a quadratic equation, x^2 - x - 2 = 0, which factors to (x - 2)(x + 1). Solving for x gives the values x = 2 and x = -1.
Step-by-step explanation:
To find the value(s) of x for which f(x) is equal to g(x), where f(x) is defined as x2 +2x +1 and g(x) as 3x+3, we need to set these two functions equal to each other and solve for x.
This gives us the equation:
x2 + 2x + 1 = 3x + 3.
To solve this equation, we first move all terms to one side to form a quadratic equation:
x2 + 2x - 3x + 1 - 3 = 0
x2 - x - 2 = 0
We can factor this quadratic equation:
(x - 2)(x + 1) = 0
Setting each factor equal to zero gives us the possible solutions for x:
- x - 2 = 0 → x = 2
- x + 1 = 0 → x = -1
Therefore, the values of x for which f(x) equals g(x) are x = 2 and x = -1.