To solve $(f - g)(-2)$, we'll first break this down into steps.

Step 1: Express $(f - g)(x)$

The operation $(f - g)(x)$ means subtracting the function $g(x)$ from $f(x)$: $(f - g)(x) = f(x) - g(x)$ Given: $f(x) = 2x^2 + 6$ $g(x) = -3x + 3$ Thus: $(f - g)(x) = (2x^2 + 6) - (-3x + 3)$ Simplifying: $(f - g)(x) = 2x^2 + 6 + 3x - 3$ $(f - g)(x) = 2x^2 + 3x + 3$

Step 2: Evaluate $(f - g)(-2)$

Now substitute $x = -2$ into $(f - g)(x)$: $(f - g)(-2) = 2(-2)^2 + 3(-2) + 3$ First, calculate each term: $2(-2)^2 = 2(4) = 8$ $3(-2) = -6$ So: $(f - g)(-2) = 8 - 6 + 3$ $(f - g)(-2) = 5$

Final Answer:

$(f - g)(-2) = 5$

Would you like further details or have any questions?

Here are some related questions you can explore:

1. What is $(f + g)(x)$ for the same functions?
2. How would you find $(f \cdot g)(x)$ at $x = 1$?
3. What is the value of $g(f(x))$ when $x = 0$?
4. Can you find where $f(x) = g(x)$?
5. What is the derivative of $(f - g)(x)$?

Tip: When combining functions, simplify the expressions carefully before substituting values!