Question

help! question written inside here

Answer 1

Find (f+g)(x),(f-g)(x), (f*g)(x), and (f/g)(x) for each f(x) and g(x). State the domain of each new function.
a. f(x)=x^2+4; g(x)=\[\sqrt{x}\]

Answer 2

b. f(x)= x-7; g(x)=x+7

Answer 3

c. f(x)=\[\sqrt{x+8}; g(x)=\sqrt{x+5}-3\]

Answer 4

\[d. f(x)= \frac{ 3 }{ x }; g(x)=x^4\]

Answer 5

@timo86m

Answer 6

im confused on this :/

Answer 7

Find (f+g)(x),(f-g)(x), (f*g)(x), and (f/g)(x) for each f(x) and g(x). State the domain of each new function.

(f+g)(x) means add the 2 functions. Also written as f(x)+g(x)
(f-g)(x) subtract the 2 functions f(x)-g(x)
(f*g)(x) means multiply the 2 functions. Also written as f(x)*g(x)
(f/g)(x) means divide f(x) by g(x). f(x)/g(x)

Domain means all x values that work. Typical examples
1/x all numbers work except for numbers that make the denominator 0. In this case 0
1/(x+1) Here -1 wont work. SO all numbers except for -1 is domain


Another type of domain example is
sqrt(x) no numbers less than zero make it not work. So you can say domain is x>=0

>= Means greater or equal to zero

Answer 8

so then like for the first one im adding x^2 and \[\sqrt{x}\]

Answer 9

******x^2+4 i mean

Answer 10

(x^2+4)+(sqrt(x)) yes I like to use parenthesis at first

Answer 11

and what would the answer be? i didnt even know you could add those two together

Answer 12

I dont think you can simplify a further so the domain is actually.
x>=0

Answer 13

so for the addition, you dont do anything right just literally add them together correct?

Answer 14

(f-g)(x) same applies here.

Answer 15

You are correct. you will add them together if they are like terms like

2x+x=3x
x^2+4x^2=5x^2
x+x+x+x=4x

Answer 16

The odd pare is the multiplication part.
(x^2+4)*(sqrt(x))
(sqrt(x))* (x^2+4) rearrange

sqrt(x)*x^2+ 4*sqrt(x) distribute the sqrt (x)


again domain will be x>=0 those are the only numbers that make it work.

I dont think i even needed to distribute the sqrt(x) here. would still work

Answer 17

for the multiplication part i got \[x^2+4\sqrt{x}\]

Answer 18

that looks wrong dude. I'll copy paste the right way from above

The odd pare is the multiplication part.
(x^2+4)*(sqrt(x))
(sqrt(x))* (x^2+4) rearrange

sqrt(x)*x^2+ 4*sqrt(x) distribute the sqrt (x)


again domain will be x>=0 those are the only numbers that make it work.

I dont think i even needed to distribute the sqrt(x) here. would still work

Answer 19

anyhoo gotta go

Answer 20

kk bye thanks anyway!