if $f(x) = 3x - 6$ and $g(x) = 6x - 3$, what is $f \cdot g$?

a. $f(x) \cdot g(x) = 6x^2 - 18x - 6$
b. $f(x) \cdot g(x) = 9x - 9$
c. $f(x) \cdot g(x) = 18x^2 - 45x + 18$
d. $f(x) \cdot g(x) = 18x + 18$

Question

if $f(x) = 3x - 6$ and $g(x) = 6x - 3$, what is $f \cdot g$?

a. $f(x) \cdot g(x) = 6x^2 - 18x - 6$
b. $f(x) \cdot g(x) = 9x - 9$
c. $f(x) \cdot g(x) = 18x^2 - 45x + 18$
d. $f(x) \cdot g(x) = 18x + 18$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Function Multiplication" ], "current_concepts": [ "Function Multiplication" ] } ## Set up the product of the functions $$ (f \cdot g)(x) = f(x) \cdot g(x) = (3x - 6)(6x - 3) $$ ## Expand the expression using FOIL $$ \begin{aligned} (3x - 6)(6x - 3) &= (3x)(6x) + (3x)(-3) + (-6)(6x) + (-6)(-3) \ &= 18x^2 - 9x - 36x + 18 \end{aligned} $$ ## Combine like terms $$ (f \cdot g)(x) = 18x^2 - 45x + 18 $$

A. $f(x) \cdot g(x) = 6x^2 - 18x - 6$

B. $f(x) \cdot g(x) = 9x - 9$

C. $f(x) \cdot g(x) = 18x^2 - 45x + 18$

D. $f(x) \cdot g(x) = 18x + 18$

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

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QUESTION IMAGE

Question

Explanation:

Set up the product of the functions

Expand the expression using FOIL

Combine like terms

Answer: