Algebra & Functions Flashcards
7 cards from real AMC 12 practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 7 Algebra & Functions flashcards as text
If f(x) = 2x + 3 and g(x) = x^2 - 1, what is f(g(2))?
Answer: 9
g(2) = 3, so f(3) = 2(3) + 3 = 9.
What is the sum of the roots of 3x^2 - 12x + 5 = 0?
Answer: 4
By Vieta's formulas the sum of roots is -b/a = 12/3 = 4.
Solve log_2(x) + log_2(x - 2) = 3.
Answer: 4
x(x - 2) = 8 gives x = 4 or x = -2, and only x = 4 keeps both logs defined.
If f(x + 1) = x^2 + 2x for all x, what is f(3)?
Answer: 8
f(x + 1) = (x + 1)^2 - 1, so f(t) = t^2 - 1 and f(3) = 8.
What is the product of the roots of x^3 - 6x^2 + 11x - 6 = 0?
Answer: 6
For a monic cubic x^3 + bx^2 + cx + d, the product of roots is -d = 6.
What is the inverse of f(x) = (2x + 1)/(x - 3)?
Answer: (3x + 1)/(x - 2)
Solving y(x - 3) = 2x + 1 for x gives x = (3y + 1)/(y - 2).
What is the minimum value of x^2 - 6x + 13?
Answer: 4
Completing the square gives (x - 3)^2 + 4, minimized at 4.
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