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College Algebra Flashcards

7 cards from real MPT practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

Read the first 7 College Algebra flashcards as text

  1. What is the inverse of the function f(x) = (x + 4)/3?

    Answer: f⁻¹(x) = 3x - 4

    Replace f(x) with y, swap x and y: x = (y+4)/3, then solve: y = 3x - 4.

  2. Solve the system: 2x + y = 7 and x - y = 2.

    Answer: x = 3, y = 1

    Add the equations: 3x = 9, so x = 3; substitute back: 3 - y = 2, y = 1.

  3. Which of the following is a rational expression in simplest form for (x² - 9)/(x - 3)?

    Answer: x + 3

    Factor the numerator: (x-3)(x+3)/(x-3) = x + 3, for x ≠ 3.

  4. The population of a town doubles every 10 years. If it starts at 5,000, what is the population after 30 years?

    Answer: 40,000

    After 30 years (3 doublings): 5,000 × 2³ = 5,000 × 8 = 40,000.

  5. What is the discriminant of 3x² - 5x + 2 = 0?

    Answer: 1

    Discriminant = b² - 4ac = (-5)² - 4(3)(2) = 25 - 24 = 1.

  6. Which inequality represents the set of x values within 3 units of 5 on the number line?

    Answer: |x - 5| < 3

    Distance from x to 5 is |x - 5|, and 'within 3 units' means |x - 5| < 3.

  7. Simplify: (2 + 3i)(1 - 2i) where i = √(-1)

    Answer: 8 - i

    Expand: 2 - 4i + 3i - 6i² = 2 - i + 6 = 8 - i, since i² = -1.