Question

Please help :) fan and medal will be given. Thank you in advance!

Left f(x) = 6x + 8 and g(x) = x^2. Perform the function operation and then find the domain of the result.
(f + g)(x)

Answer 1

`(f + g)(x)` is equivalent to saying `f(x) + g(x)`

Answer 2

perform substitutions and rearrange terms to get it into standard form

Answer 3

Okay, thank you! Can you show me how to set it up please? I'm sorry, I know I should know this, but I get confused.

Answer 4

here's an example

f(x) = 9x+17
g(x) = 3x^2


(f+g)(x) = f(x) + g(x)
(f+g)(x) = 9x+17 + g(x)
(f+g)(x) = 9x+17 + 3x^2
(f+g)(x) = 3x^2 + 9x+17


In step 1, I used the definition of what (f+g)(x) represents
In step 2, I replaced f(x) with 9x+17, since they are equivalent
In step 3, I replaced g(x) with 3x^2, since they are equivalent
In step 4, I rearranged the terms to get the polynomial into standard form


this is NOT the answer since it's just an example; however, this should hopefully help you out since it's a similar problem

Answer 5

Thank you very much!!!! It does help :) I'm gonna look over it more and apply the steps to the actual problem I'm working on and see if I can get the right answer. I'm also going to go ahead and give you the best answer :) thank you for helping me!

Answer 6

\(\bf f(x) = 6x + 8 \qquad g(x) = x^2
\\ \quad \\
(f+g)(x)\implies f(x)+g(x)\implies (6x + 8)\quad +\quad (x^2)\)

Answer 7

you're welcome

Answer 8

let me know if you're stuck on how to find the domain

Answer 9

I will :) thank you, again

Answer 10

Is it x2 + 6x + 17?

Answer 11

no

Answer 12

idk where you got the 17 from

Answer 13

the problem gives ` f(x) = 6x + 8 and g(x) = x^2` right?

Answer 14

Yes! Sorry for the late reply.

Answer 15

so it should be x^2+6x+8

Answer 16

Yes, sorry! I meant 8. I got the example confused with the other problem.

Answer 17

that's ok

Answer 18

And the domain is a set of all real numbers, correct? Or am I wrong?

Answer 19

yep, the domain of f(x) is the set of all real numbers
the domain of g(x) is the set of all real numbers
the domain of (f+g)(x) is the set of all real numbers

Answer 20

why? because each is a polynomial

Answer 21

Awesome! Yay ^.^ thank you :)

I have another problem, Let f(x) = x-2 and g(x) = 4x^2. Perform the function operation and then find the domain of the result. Would I apply the exact steps that you showed me from before? :)

Answer 22

which operation? it doesn't say

I'm guessing (f+g)(x) ? but again, it doesn't specify the operation

Answer 23

Oh, sorry! I forgot to put that. No, the operation is (f-g)(x)

Answer 24

we are given
\[\Large {\color{red}{f(x)}} = {\color{red}{x-2}}\]
\[\Large {\color{blue}{g(x)}} = {\color{blue}{4x^2}}\]
and we want to find
\[\Large (f-g)(x)\]

Answer 25

Yes

Answer 26

so...
\[\Large (f-g)(x) = f(x) - g(x)\]
\[\Large (f-g)(x) = {\color{red}{f(x)}} - {\color{blue}{g(x)}}\]
\[\Large (f-g)(x) = ({\color{red}{f(x)}}) - ({\color{blue}{g(x)}})\]
\[\Large (f-g)(x) = ({\color{red}{x-2}}) - ({\color{blue}{4x^2}})\]
I'll let you finish up

Answer 27

f = - 3x^2 - gx - x + 2 /x?

Answer 28

huh? is this a different problem?