if $c(x) = 4x - 2$ and $d(x) = x^2 + 5x$, what is $(c \circ d)(x)$?

* $4x^3 + 18x^2 - 10x$
* $x^2 + 9x - 2$
* $16x^2 + 4x - 6$
* $4x^2 + 20x - 2$

Question

if $c(x) = 4x - 2$ and $d(x) = x^2 + 5x$, what is $(c \circ d)(x)$?

* $4x^3 + 18x^2 - 10x$
* $x^2 + 9x - 2$
* $16x^2 + 4x - 6$
* $4x^2 + 20x - 2$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Composite Functions" ], "new_concepts": [], "current_concepts": [ "Composite Functions" ] } ## Define the composite function expression $$ (c \circ d)(x) = c(d(x)) $$ ## Substitute the inner function $$ (c \circ d)(x) = c(x^2 + 5x) $$ ## Evaluate the outer function and simplify $$ \begin{aligned} (c \circ d)(x) &= 4(x^2 + 5x) - 2 \ &= 4x^2 + 20x - 2 \end{aligned} $$

(A) $4x^3 + 18x^2 - 10x$

(B) $x^2 + 9x - 2$

(C) $16x^2 + 4x - 6$

(D) $4x^2 + 20x - 2$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Composite Functions" ] }

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QUESTION IMAGE

Question

Explanation:

Define the composite function expression

Substitute the inner function

Evaluate the outer function and simplify

Answer: