if $f(x) = x^2 - 2x$ and $g(x) = 6x + 4$, for which value of $x$ does $(f + g)(x) = 0$?

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-2
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Question

if $f(x) = x^2 - 2x$ and $g(x) = 6x + 4$, for which value of $x$ does $(f + g)(x) = 0$?

-4
-2
2
4

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Function Addition" ], "new_concepts": [ "Solving Quadratic Equations" ], "current_concepts": [ "Function Addition", "Solving Quadratic Equations" ] } ## Define the sum function $$ (f+g)(x) = f(x) + g(x) = (x^2 - 2x) + (6x + 4) $$ ## Simplify the expression $$ (f+g)(x) = x^2 + 4x + 4 $$ ## Solve for x when the sum is zero $$ \begin{aligned} x^2 + 4x + 4 &= 0 \ (x + 2)^2 &= 0 \ x &= -2 \end{aligned} $$

-4

-2

2

4

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Function Addition" ] }

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QUESTION IMAGE

Question

Explanation:

Define the sum function

Simplify the expression

Solve for x when the sum is zero

Answer: