Final answer:
The value of (g - f)(-2), where f(x) = 2x^2 and g(x) = 2 - 3x, is 0. To find this, the expression (g - f)(x) = 2 - 3x - 2x^2 is evaluated at x = -2 resulting in a final answer of 0.
Step-by-step explanation:
The student is asking for the value of the function (g - f)(-2). Given two functions, f(x) = 2x^2 and g(x) = 2 - 3x, we need to subtract f(x) from g(x) and then evaluate the resulting function at x = -2.
First, let's find the expression for (g - f)(x):
- g(x) = 2 - 3x
- f(x) = 2x^2
- (g - f)(x) = g(x) - f(x) = (2 - 3x) - (2x^2)
Now we simplify the expression:
- (g - f)(x) = 2 - 3x - 2x^2
Next, we evaluate (g - f)(-2):
- (g - f)(-2) = 2 - 3(-2) - 2(-2)^2
- (g - f)(-2) = 2 + 6 - 8
- (g - f)(-2) = 0
Therefore, the value of (g - f) (-2) is 0.