let $f(x) = x^2 - 1$ and $g(x) = 4x - 2$. find the value, if possible. (if not possible, enter impossible.)
$(f + g)(-2)$
$(f + g)(-2) =$

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Function Addition" ], "new_concepts": [], "current_concepts": [ "Function Addition", "Evaluating Functions Graphically" ] } ## Apply the definition of function addition $$ (f + g)(-2) = f(-2) + g(-2) $$ ## Evaluate each function at the given input $$ \begin{aligned} f(-2) &= (-2)^2 - 1 = 4 - 1 = 3 \ g(-2) &= 4(-2) - 2 = -8 - 2 = -10 \end{aligned} $$ ## Sum the evaluated values $$ (f + g)(-2) = 3 + (-10) = -7 $$ Let $f(x) = x^2 - 1$ and $g(x) = 4x - 2$. Find the value, if possible. (If not possible, enter IMPOSSIBLE.) $(f + g)(-2) =$ -7 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Function Addition" ] }

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Explanation:

Apply the definition of function addition

Evaluate each function at the given input

Sum the evaluated values

Answer: