if $p(x) = x^2 - 1$ and $q(x) = 5(x - 1)$, which expression is equivalent to $(p - q)(x)$?

* $5(x - 1) - x^2 - 1$
* $(5x - 1) - (x^2 - 1)$
* $(x^2 - 1) - 5(x - 1)$
* $(x^2 - 1) - 5x - 1$

Question

if $p(x) = x^2 - 1$ and $q(x) = 5(x - 1)$, which expression is equivalent to $(p - q)(x)$?

* $5(x - 1) - x^2 - 1$
* $(5x - 1) - (x^2 - 1)$
* $(x^2 - 1) - 5(x - 1)$
* $(x^2 - 1) - 5x - 1$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Function Subtraction" ], "new_concepts": [], "current_concepts": [ "Function Subtraction" ] } ## Define the function subtraction operation $$ (p - q)(x) = p(x) - q(x) $$ ## Substitute the given function expressions $$ \begin{aligned} p(x) &= x^2 - 1 \ q(x) &= 5(x - 1) \ (p - q)(x) &= (x^2 - 1) - 5(x - 1) \end{aligned} $$

(A) $5(x-1) - x^2 - 1$

(B) $(5x-1) - (x^2-1)$

(C) $(x^2-1) - 5(x-1)$

(D) $(x^2-1) - 5x - 1$

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

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Question

Explanation:

Define the function subtraction operation

Substitute the given function expressions

Answer: