Domain


Key things to look at when finding domain with a function involving square roots.
Ø Square roots cannot be negative


Ex. Pg 132 #28
K(x)= x^2+1 set the function as an equality

X^2+1>0 anything times its self is positive so the domain of this function is all real numbers.


Ex. Pg 132 # 27
H(x)= 2-x set the function up as an equality

2-x >= 0 subtract –2 from both sides
-2 -2
-x >= -2 divide by –1 and since you are dividing by a negative the inequality sing flips
-1 -1
x <= 2

Ex. Pg 130 #25

F(x)= ` X `
X^2 * 2X factor the denominator

F(x)= ` X `
X (X-2) set the denominator equal to 0

X (X-2) =0
X=0
X-2=0
+2 +2
X=2
So X cannot equal 0 or 2 because then the denominator is 0

Key things to remember are no negatives under a radical and the denominator cannot equal 0.





Piecewise

Important thing to remember is that you find the value that the two functions share.

F(x) { radical over 1-x if x<1
X^2-1 if x>= 1 plug in 1 into both functions

Radical over 1-1=0
1^2-1=0


Homework
9/12/07
pg 155 #1-10 even, 33-42even 43-52even