Algebraic Equations and Functions Flashcards

If f(x) = x² and g(x) = x + 1, what is f(g(2))?

Answer: 9

g(2) = 3, then f(3) = 9.

Solve the inequality: 3x - 5 > 7.

Answer: x > 4

Add 5 to get 3x > 12, then divide by 3 to get x > 4.

Using the quadratic formula, what are the solutions to x² - 5x + 6 = 0?

Answer: x = 2, 3

The equation factors as (x - 2)(x - 3) = 0, giving x = 2 and x = 3.

Simplify: x⁸ / x³.

Answer: x⁵

When dividing like bases, subtract exponents: 8 - 3 = 5.

If the function f(x) = |x - 3|, what is f(1)?

Answer: 2

f(1) = |1 - 3| = |-2| = 2.

What value of k makes x² + kx + 9 a perfect square trinomial?

Answer: 6

A perfect square (x + 3)² = x² + 6x + 9 requires k = 6.

If y varies directly with x and y = 12 when x = 4, what is y when x = 7?

Answer: 21

The constant is 12/4 = 3, so y = 3(7) = 21.