use the graphs of f and g to evaluate the composite function.
$(f \circ g)(-3)$

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Function Composition" ], "new_concepts": [], "current_concepts": [ "Function Composition", "Evaluating Functions from Graphs" ] } ## Define the composite function Using the *Function Composition* knowledge point $$ (f \circ g)(-3) = f(g(-3)) $$ ## Evaluate the inner function from the graph Using the *Function Composition* knowledge point $$ \begin{aligned} &\text{Find } x = -3 \text{ on the red line } y = g(x).\ &g(-3) = -1 \end{aligned} $$ ## Evaluate the outer function from the graph Using the *Function Composition* knowledge point $$ \begin{aligned} &\text{Substitute } g(-3) = -1 \text{ into } f(g(-3)).\ &f(g(-3)) = f(-1)\ &\text{Find } x = -1 \text{ on the blue curve } y = f(x).\ &f(-1) = 5 \end{aligned} $$ Use the graphs of f and g to evaluate the composite function. $(f \circ g)(-3) =$ $5$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Function Composition" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Define the composite function

Evaluate the inner function from the graph

Evaluate the outer function from the graph

Answer: