1a. Compare methods of solving linear equations and methods of solving linear inequalities. What
do they have in common? What is different?
The methods of solving both the linear equalities and inequalities are almost similar, the only difference is
that
1. What is a composition of functions? What is the difference between the composition
and the product of two functions?
Composition of two function
let f ( x) and g( x) are two function
composition of function is f of
Example: f ( x )=x 2 +2; g ( x )=x +
1. What is the geometric sense of a linear system in two variables and a linear system in
three variables?
For a system involving two variables (x and y), each linear equation determines a line on the xyplane. Because a solution to a linear system must sa
Chapter 4
Section 4.1
1
7
1
#21: f ( x )=2 x+ 7 ; f ( x ) = x
2
2
1
1
f ( f ( x ) ) =xf ( f ( x ) ) =x
1
7
f ( f 1 ( x ) ) =2 x +7=x7+7=x
2
2
1
7
7 7
f 1 ( f ( x ) )= ( 2 x+ 7 ) =x + =x
2
2
2 2
1
f ( x )f ( x ) are inverse of one another
(
)
1
1
#23: f
Chapter 9 section 9.1
In Exercises 5 to 24, solve each system of equations by
using the substitution method.
x5
cfw_ y=3
y=5 x7
#15:
In Exercises 25 to 42, solve each system of equations by
using the elimination method.
#31:
cfw_63xx+2y=4
y=8
#37:
cfw_
3
1. Explain why trigonometric functions are periodic.
There are many cases in which more than one angle has the same value for its sine, cosine, or
some other trigonometric function. This phenomenon exists because all trigonometric functions
are periodic.