Question

Let f(x) = 3x - 6 and g(x) = x - 2. Find and its G/H domain

Answer 1

A. 3; all real numbers except x = 2

B. 3; all real numbers

C. -3; all real numbers except x = 3

D. 1; all real numbers

Answer 2

what is the first thing we have to find ?

Answer 3

oppps find F/G and its domain

Answer 4

\[ \frac{3x - 6}{x-2} \]

can you factor 3 from the expression in the numerator?

Answer 5

I have noo idea.. sorry I'm lost with all this stuff.. :/

Answer 6

The idea is like this:

say you have two things a + b grouped together (i.e. added)

and we have 3 of these groups: 3(a+b)
3(a+b) means 3 times (a+b)

if you have 3 of these "packages" it should be more or less obvious we have 3 of each thing inside the package:

3(a+b) = 3a + 3b

factoring "undoes" the 3a + 3b
if you can evenly divide both terms by 3 you can rewrite
3a+3b as 3(a+b)

Answer 7

in your case, you have 3x -6
notice both terms can be divided evenly by 3

Answer 8

Right

Answer 9

can you try to factor 3 out of 3x - 6 ?

Answer 10

I'm not really sure how to write it because theres only an X without any numbers next to it.. soo idk how to factor them together..

Answer 11

3x/3 is x
-6 /3 is -2

you get x-2 for the part that goes in the parens

Answer 12

3(x-2) ?

Answer 13

yes.

you now have
\[ \frac{3(x-2)}{(x-2)} \]

Answer 14

okay

Answer 15

I assume you know anything divided by itself is 1 (except 0/0 which we are not allowed to do)

Answer 16

right.. so the answer would be 3

Answer 17

(x-2) divided by itself is 1

the only exception is it is not allowed to be 0
in other words, we do NOT want x-2= 0
i.e. x=2 is not allowed

Answer 18

for all values of x except x=2, we get 3
(you can test a few values to see it really works)

but for x=2 we run into a problem of dividing by 0. so we make a note: no divide by 0
or in other words, x ≠ 2

Answer 19

btw, the "domain" are all the x values we are allowed to use.
we can use any number except x=2

Answer 20

Okay so were left with 1?

Answer 21

WAIT! I get it... itd be A?
3; all real numbers except x = 2

Answer 22

yes

Answer 23

lol thank you =]

Answer 24

yw