Question

Someone- anyone please help

Suppose that the functions of f and g are as follows
f(x) = 2x+3
g(x)= (sqrt 4x-5)
Find f*g and f+g. Then give their domain using interval notation

(f*g)(x)=
Domain of f*g:

(f+g)(x)=
Domain of f+g:

Answer 1

So this is what I got for (f*g)= 2x(sqrt)4x-5 + 3(sqrt)4x-5 for f+g= 2x+3+(sqrt)4x-5 is that right?

Answer 2

\[f(x)\times g(x)=(2x+3)(\sqrt{4x-5})\]

Answer 3

gotcha mertsj: So that is the answer doesn't factor out to something that I can write into interval notation like. [2,3] U [5/4, infinity)? right?

Answer 4

You have to tell the set of acceptable x values. In other words, the radicand must be >=0.
So solve 4x-5>=0

Answer 5

I think the original equation looks wrong \[f(x)= 2x+3 and g(x)= \sqrt{4x-5}\]

Answer 6

geesh- i loath this stuff!

Answer 7

it's like climbing a rope made of water for me#beating head on wall

Answer 8

I guess I don't know what you are saying because we used f(x)=2x+3 and g(x)=sqrt(4x-5) for our functions.

Answer 9

Thats right in the original equation- I just wasn't sure if I put the sqrt in the right way. you got it right

Answer 10

so when I solve 4x-5>0 I get x>5/4. So since there can't be a negative in a sqrt. I have [5/4,infinity) as it's written in interval notation... correct....

Answer 11

yes

Answer 12

:)

Answer 13

So for f(x) +g(x) I get 2x+3+(sqrt)4x-5

Answer 14

yes

Answer 15

sqrt(4x-5)

Answer 16

So what is the domain?

Answer 17

AWESOME!!!
so the domain of both (f+g)(x) and (f*g)(x)= [5/4,infinity) because that's where they intersect... Fingers crossed- correct?

Answer 18

Has nothing to do with intersection. The domain is the set of legal x values and in both of these functions it is the same set because the radicand must be greater than 0

Answer 19

gotcha

Answer 20

So my answer is
f(x)×g(x)= 5/4
domain: [5/4,infinity)

and for f(x)+g(x)= 5/4
[5/4,infinity)

Answer 21

\[f(x)*g(x)=(2x+3)(\sqrt{4x-4})\]

Answer 22

\[D=[\frac{5}{4},\infty )\]

Answer 23

\[f(x)+g(x)=2x+3+\sqrt{4x-5}\]

Answer 24

\[D=[\frac{5}{4},\infty )\]

Answer 25

Mertsj: you are awesome- I'll try to get this worked into my brain someway. Thank you for your time and efforts- I sincerely appreciate it, you have no idea how hard this stuff is. I'm just glad that there are people out there like you that helps people like me. I would pay you if I could. Cheers :)

Answer 26

I know it is hard but if you keep at it, you will get it. Think how many times your mom had to say your name to you before you learned it!!!