Question

What is (f+g)(x)?

f(x)=x3−x

g(x)=x3+2x2−10

Answer 1

(f+g)(x) just means add f(x) and g(x)

so let's start with combining the only like terms there are

x^3 + x^3 = ?

Answer 2

x^6 i think bc 3+3

Answer 3

that's a good guess but not quite ^^

it's really no different than adding two objects, object + object = 2 objects

so x^3 + x^3 = 2x^3

Answer 4

ohh okay

Answer 5

*** - 10 not + 10

Answer 6

2x^3 + 2x^2 - x - 10 = your answer [there's no edit button]

Answer 7

oh okay so just minus 10 instead of +

Answer 8

at the end

Answer 9

yup

Answer 10

alright thx so much !

Answer 11

so would it be the same thing if it was (f*g)(x) instead of (f+g)(x)? @Vocaloid

Answer 12

What is (f⋅g)(x)?



f(x)=x2+2x−6

g(x)=x4+3

Answer 13

x^2+x^4 would it be like 2x^6 or adding the exponents

Answer 14

the ⋅ means multiply

so you would have to multiply

(x^2+2x−6)(x^4+3) using the distributive property, know how to start w/ this?

Answer 15

oh would it be like foil

Answer 16

sort of but the first parentheses have 3 terms so it's a bit different than foil

Answer 17

let's just start with the first term

what's x^2 * x^4 = ?

Answer 18

x^6?

Answer 19

is it x^6+2x-18

Answer 20

bc 2x doesn't have a like term and then -3*6 = -18

Answer 21

since we're multiplying we have to consider all terms unfortunately

Answer 22

oh ok oops

Answer 23

multiplying the first terms gives us x^6

multiplying the next terms gives us 2x^3

then we need to keep going

Answer 24

*** should be 3x^2

Answer 25

oh ok so every term in the first paratheses multiplies by every term in the second one

Answer 26

yeah, then the last term in the first parentheses * every term in the second parentheses

Answer 27

then just putting everything together:

x^6 + 3x^2 + 2x^5 + 6x - 6x^4 - 18

then just re-arrange so that the exponents decrease from highest to lowest

x^6 + 2x^5 - 6x^4 + 3x^2 + 6x - 18 = your final answer

Answer 28

okay thanks again if i could give you another medal i would lol

Answer 29

"What is (f⋅g)(x)?"

This is a composition.

- That is, if you intend that (f⋅g)(x) be \((f \circ g)(x)\)

- Then:

\((f \circ g)(x) = f(g(x))\)

Answer 30

I thought of that possibility but doesn't a closed dot usually indicate multiplication? :S

Answer 31

it surely does

Answer 32

i was over -thinking it :(