solve the inequality $\sqrt3{x+4} \sqrt3{-x}$. a) $x 2$ c) $x -2$ question 5 (5 points) let $f(x) = x^2 + 2x$ and $g(x) = 2x$. evaluate the composition $(f \cdot g)(2)$. a) $(f \cdot g)(2) = 32$ b) $(f \cdot g)(2) = 24$ c) $(f \cdot g)(2) = 16$ d) $(f \cdot g)(2) = 48$ question 6 (5 points) whats the inverse of $f(x) = x - 20$? a) $f^{-1}(x) = x + 20$ b) $f^{-1}(x) = 20x$ c) $f^{-1}(x) = \sqrt5{\frac{x}{20}}$ d) $f^{-1}(x) = \frac{x}{20}$

Question

solve the inequality $\sqrt3{x+4} > \sqrt3{-x}$. a) $x < 2$ b) $x > 2$ c) $x < -2$ d) $x > -2$ question 5 (5 points) let $f(x) = x^2 + 2x$ and $g(x) = 2x$. evaluate the composition $(f \cdot g)(2)$. a) $(f \cdot g)(2) = 32$ b) $(f \cdot g)(2) = 24$ c) $(f \cdot g)(2) = 16$ d) $(f \cdot g)(2) = 48$ question 6 (5 points) whats the inverse of $f(x) = x - 20$? a) $f^{-1}(x) = x + 20$ b) $f^{-1}(x) = 20x$ c) $f^{-1}(x) = \sqrt5{\frac{x}{20}}$ d) $f^{-1}(x) = \frac{x}{20}$

Accepted Answer

{ "quality": "clear", "question_count": 3, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Function Composition", "Inverse Relations" ], "new_concepts": [ "Radical Inequalities" ], "current_concepts": [ "Radical Inequalities", "Function Composition", "Inverse Relations" ] } ## Solve the radical inequality $$ \begin{aligned} &\sqrt[3]{x+4} > \sqrt[3]{-x} \ &x+4 > -x \ &2x > -4 \ &x > -2 \end{aligned} $$ ## Evaluate the function composition $$ \begin{aligned} &g(2) = 2(2) = 4 \ &(f \cdot g)(2) = f(g(2)) = f(4) \ &f(4) = 4^2 + 2(4) = 16 + 8 = 24 \end{aligned} $$ ## Find the inverse function $$ \begin{aligned} &y = x - 20 \ &x = y + 20 \ &f^{-1}(x) = x + 20 \end{aligned} $$ ## Question 1 (A) $x < 2$

(B) $x > 2$

(C) $x < -2$

(D) $x > -2$ ## Question 2 (A) $(f \cdot g)(2) = 32$

(B) $(f \cdot g)(2) = 24$

(C) $(f \cdot g)(2) = 16$

(D) $(f \cdot g)(2) = 48$ ## Question 3 (A) $f^{-1}(x) = x + 20$

(B) $f^{-1}(x) = 20x$

(C) $f^{-1}(x) = \sqrt[x]{20}$

(D) $f^{-1}(x) = \frac{x}{20}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Function Composition and Inverses" ] }

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QUESTION IMAGE

Question

Explanation:

Solve the radical inequality

Evaluate the function composition

Find the inverse function

Answer:

Question 1

Question 2

Question 3