Rational & Radical Expressions
Solve: (1/x) + (2/(x+1)) = 3
x = ±1
i³ × i⁴ =
-i
How many complex roots in f(x) = x⁴ + 1?
4 complex roots
Inverse of f(x) = 3x - 1
f⁻¹(x) = (x + 1)/3
Vertex form of y = x² - 6x + 5
Vertex: (3, -4)
Simplify: √(50)
5√2
Complete the square: x² + 6x = 7
x = 1 or -7
Find zeros: f(x) = x² - 3x + 2
x = 1 or 2
Solve: 2^x = 16
x = 4
Identify asymptotes: f(x) = 1/(x+2)
Vertical asymptote at x = -2; horizontal at y = 0
Add: 2√3 + 4√3
6√3
Solve: x² - 4x - 5 = 0
x = 5 or -1
What does the Fundamental Theorem of Algebra state?
Every non-zero polynomial equation of degree n has exactly n complex roots (including multiplicity).
log₃(81) =
4
Equation of ellipse: center (0,0), a=4, b=3
x²/16 + y²/9 = 1
Rationalize: 1/√2
√2/2
Solve: x² + 3x > 10
x < -5 or x > 2
f(x) = 2x + 3, g(x) = x². Find f(g(x))
2x² + 3
Properties: log(ab) = ?
log a + log b
Period of y = 3sin(x)
2π
Solve: √(x + 2) = 5
x = 23
Find zeros: f(x) = x² - x - 6
x = 3 or -2
Is f(x) = x³ + 2x a polynomial? Why?
Yes, all powers are non-negative integers
Solve: log(x+2) = 1
8
cos(2θ) in terms of sin²θ
1 - 2sin²θ