homework

1.) given that $f(x) = 2x + 1$, $g(x) = x^2$
find $(f \cdot g)(x)$ b) $(g \cdot f)(x)$

2.) if $f(x) = 3x - 4$ and $g(x) = x + 2$ find $(f \cdot g)(5)$

Question

homework

1.) given that $f(x) = 2x + 1$, $g(x) = x^2$
find $(f \cdot g)(x)$ b) $(g \cdot f)(x)$

2.) if $f(x) = 3x - 4$ and $g(x) = x + 2$ find $(f \cdot g)(5)$

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Function Operations", "Function Evaluation" ], "new_concepts": [], "current_concepts": [ "Function Operations", "Function Evaluation", "Composite Functions" ] } ## Find the product and composition functions for Question 1 $$ \begin{aligned} (f \cdot g)(x) &= f(x) \cdot g(x) = (2x + 1)(x^2) = 2x^3 + x^2\ (g \cdot f)(x) &= g(x) \cdot f(x) = (x^2)(2x + 1) = 2x^3 + x^2 \end{aligned} $$ ## Evaluate the product function at x = 5 for Question 2 $$ \begin{aligned} (f \cdot g)(x) &= f(x) \cdot g(x) = (3x - 4)(x + 2)\ (f \cdot g)(5) &= f(5) \cdot g(5) = (3(5) - 4)(5 + 2) = (11)(7) = 77 \end{aligned} $$ ## Question 1 $$ \begin{aligned} (f \cdot g)(x) &= 2x^3 + x^2\ (g \cdot f)(x) &= 2x^3 + x^2 \end{aligned} $$ ## Question 2 $$ (f \cdot g)(5) = 77 $$ { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Function Operations" ] }

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QUESTION IMAGE

Question

Explanation:

Find the product and composition functions for Question 1

Evaluate the product function at x = 5 for Question 2

Answer:

Question 1

Question 2