let $f(x) = x + 1$ and $g(x) = 5x$. evaluate the composition $(f \cdot g)(-1)$.

a) $(f \cdot g)(-1) = 4$
b) $(f \cdot g)(-1) = -4$
c) $(f \cdot g)(-1) = -6$
d) $(f \cdot g)(-1) = 6$

question 14 (5 points)
solve the equation: $\sqrt{x^2 + 4} - 1 = 2$

a) $x = 3$
b) $x = 5$
c) $\pm x = \sqrt{5}$
d) $\pm x = \sqrt{13}$

question 15 (5 points)
solve the equation $10 + \sqrt{y} = 14$

a) $y = 4$
b) $y = 2$
c) $y = 16$
d) $y = 576$

Question

let $f(x) = x + 1$ and $g(x) = 5x$. evaluate the composition $(f \cdot g)(-1)$.

a) $(f \cdot g)(-1) = 4$
b) $(f \cdot g)(-1) = -4$
c) $(f \cdot g)(-1) = -6$
d) $(f \cdot g)(-1) = 6$

question 14 (5 points)
solve the equation: $\sqrt{x^2 + 4} - 1 = 2$

a) $x = 3$
b) $x = 5$
c) $\pm x = \sqrt{5}$
d) $\pm x = \sqrt{13}$

question 15 (5 points)
solve the equation $10 + \sqrt{y} = 14$

a) $y = 4$
b) $y = 2$
c) $y = 16$
d) $y = 576$

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" ], "new_concepts": [ "Radical Equations" ], "current_concepts": [ "Function Composition", "Radical Equations", "Solving Radical Equations" ] } ## Evaluate the function composition $$ \begin{aligned} g(-1) &= 5(-1) = -5 \ (f \circ g)(-1) &= f(g(-1)) = f(-5) = -5 + 1 = -4 \end{aligned} $$ ## Solve the first radical equation $$ \begin{aligned} \sqrt{x^2 + 4} - 1 &= 2 \ \sqrt{x^2 + 4} &= 3 \ x^2 + 4 &= 9 \ x^2 &= 5 \ x &= \pm\sqrt{5} \end{aligned} $$ ## Solve the second radical equation $$ \begin{aligned} 10 + \sqrt{y} &= 14 \ \sqrt{y} &= 4 \ y &= 16 \end{aligned} $$ ## Question 1 (A) $(f \cdot g)(-1) = 4$

(B) $(f \cdot g)(-1) = -4$

(C) $(f \cdot g)(-1) = -6$

(D) $(f \cdot g)(-1) = 6$ ## Question 2 (A) $x = 3$

(B) $x = 5$

(C) $\pm x = \sqrt{5}$

(D) $\pm x = \sqrt{13}$ ## Question 3 (A) $y = 4$

(B) $y = 2$

(C) $y = 16$

(D) $y = 576$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Radical Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Evaluate the function composition

Solve the first radical equation

Solve the second radical equation

Answer:

Question 1

Question 2

Question 3