\f(x) = x^2 + 1\

what is $f(f(x))$?

* $x^4 + 2x^2 + 1$
* $x^4 + 2x^2 + 2$
* $x^4 + 2$
* $x^4 + 1$

Question

\f(x) = x^2 + 1\

what is $f(f(x))$?

* $x^4 + 2x^2 + 1$
* $x^4 + 2x^2 + 2$
* $x^4 + 2$
* $x^4 + 1$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Composite Functions", "Polynomial Operations" ], "new_concepts": [], "current_concepts": [ "Composite Functions", "Polynomial Operations" ] } ## Substitute the inner function Using the *Composite Functions* knowledge point $$ f(f(x)) = f(x^2 + 1) $$ ## Expand and simplify the expression Using the *Polynomial Operations* knowledge point $$ \begin{aligned} f(x^2 + 1) &= (x^2 + 1)^2 + 1 \ &= (x^4 + 2x^2 + 1) + 1 \ &= x^4 + 2x^2 + 2 \end{aligned} $$

(A) $x^4 + 2x^2 + 1$

(B) $x^4 + 2x^2 + 2$

(C) $x^4 + 2$

(D) $x^4 + 1$

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

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QUESTION IMAGE

Question

Explanation:

Substitute the inner function

Expand and simplify the expression

Answer: