Question

Suppose we are given two functions, say r(x) and s(x).
a) Is it true that r(x) + s(x) = s(x) + r(x) for all values of x? Why or why not?
b) Is it true that r(x)

Answer 1

i lost you.

Answer 2

Addition and multiplication are both commutative (meaning you can switch the order of them)...

It's not always true that r(0) = 0. if r(x) = x +1, then r(0) = 0+1 = 1

Answer 3

That was a old problem i was working on. What happen to the last one?

Answer 4

i was lagging...probably because of the size of the post :(

Answer 5

we can continue here though...

Answer 6

Oh. You have been so helpful!

Answer 7

so let's recap...you need to find g(a) - g(a-b) + f(a)...

Answer 8

where g(a) = 2-3x and f(x) = 3x+2-(4/x), right?

Answer 9

yes

Answer 10

and we have established that...

Answer 11

g(a) = 2-3a and g(a-b) = 2-3a+3b, right?

Answer 12

right

Answer 13

so...what is f(a)?

Answer 14

and don't let the fraction scare you... ;)

Answer 15

f(a)=3a+2-4/a?

Answer 16

exactly!

Answer 17

really?

Answer 18

now...let's put them together, distribute any negatives, and simplify.

Answer 19

Ok so how do i write this out the right way?

Answer 20

\[g(a)-g(a-b)+f(a)=(2-3x)-(2-3a+3b)+(3a+2-\frac{4}{a})\]

Answer 21

distribute the negative in the middle and combine like terms...

Answer 22

ack...change the x to an a....

Answer 23

uhh. yikes. ok.

Answer 24

i dont know.

Answer 25

you should get\[2-3a-2+3a-3b+3a+2-\frac{4}{a}\]after changing the signs of the middle grouping...

Answer 26

thats the answer?

Answer 27

eanotice that each set of parenteses is just what we found to be g(a), g(a-b) and f(a)...

Answer 28

no...now you need to combine like terms...combine things with an a together and combine things with a b together...

Answer 29

anything that is just a number can combine as well..

Answer 30

for instance, the first and second 2 cancel each other, right?

Answer 31

-3b+3a+2-4/a?

Answer 32

ya

Answer 33

and tyou say you aren't good at math! i think you lied to me :)

Answer 34

haha the fact that they canceled out was worryin me

Answer 35

so now you got it, right? :)

Answer 36

yes. wow. that helped so much.

Answer 37

then it's time for me to depart...if you see me on and have more question, let me know.

Answer 38

Thank you!! I will!!

Answer 39

my pleasure.