mathematics

MATH 112 Fall 2018 - GHW 2 Part 2 Name _________________________________________________ This GHW is due by 3:00 pm on Thursday, October 4. This GHW can be turned in during class on Wednesday if you like, but if not, you can drop it off at my office (ECC 240). If I am not there, just slide it under the door. You may discuss this assignment with others in the class or with me, but the work that you turn in must be your own write-up. For each of the following problems, supporting work is necessary for credit (unless stated otherwise). Supporting work must be presented in a complete, neat and orderly fashion. This includes the use of correct notation. Put your work and answers (unless stated otherwise) on one side of separate standard size sheets of paper. Your work must be stapled (in the upper left-hand corner) to this sheet with this sheet being the first page, and with the problems given in order. Be sure to justify and simplify your answers. Remember to use pencil. Express all numerical answers using exact values. Give concluding statements for each (part of) the following problems.

1. Determine the domain of the function 3 2

1 0 3 ( )

2 8

x f x

x x x

 

 

. Express the domain using interval notation.

2. Let ( ) 2 3f x x  on [ 6 , 4 ) f

D   and ( ) 2 1g x x  on [ 2 , 8 ) g

D   .

For each of the following, be sure to simplify the resulting rules and express the domains using interval notation

when appropriate. Label quantities and use correct notation.

a) Find the domain and rule for f g .

b) Find the domain and rule for /g f .

c) Find the domain and rule for f g .

d) Find the domain and rule for g f .

3. Let f be the function given by 7 1 4

( ) 2 3

x f x

x

 

 on (2 , 5 ]

f D  . It is also know that [ 2 1 , 9 )fR    .

Find 1 ( )f x  (both the domain and the rule), if it exists.

4. Determine if 2 23 3 2 3 3 0x y x y     represents a circle. If the equation represents a circle, put the equation in

standard form and find the center and radius of the circle.

5. Solve 4 3 23 0 3 6 0x x x   algebraically for x. Be sure to express the solution using set notation.