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Chp 1: Find Domain of x (Complex # set (standard form a+bi, Conjugates…
Chp 1: Find Domain of x
Absolute Values
Solutions are +/-
abs equations
2 solutions
check
abs inequalities
|u| > a =
u > a & -u < a
Don't forget union sign
|u|<a =
-a<u<a
Complex # set
standard form a+bi
Conjugates produce real numbers
patterns of i
Special product formula for (x+a)^3
Quadratic formula +/-
Principal sq root of -N
Radical
Sq by index
Often becomes quadratic
check solution
if index and radicand same, divide both by lcm
Linear Equations
zero-product property
LCM
check
Quadratic Equations
Complete the sq
check
Factoring
Sq root method
check
Zero-product property
Quadratic formula
check discriminant
Quadratic in form
Sub x for u
works for radicals
Keep factoring
Inequalities
Equivalent inequalities
get same x
reciprocal property
must be inqeual to 0
Numerator must be 1
Sign changing with negatives
Interval()[] and Set notation 0<x<1
Radical; acts like an abs value
Combined inequalities
Separate them if needed