Question

Given that f(x)=sqrt{2 + x} and g(x)=sqrt{2 - x}, find formulas for the following functions, and their domains. In each case, enter the domain using interval notation.

(a) f+g= and its domain is

Answer 1

Have you searched the web? I havn't studied this yet /:

Answer 2

I have.. I can't find anything similar :/

Answer 3

@qpHalcy0n can you help me?

Answer 4

@jim_thompson5910 can you please help? :)

Answer 5

f(x) + g(x) literally means "add the functions f(x) and g(x)"

Answer 6

but since f(x) = sqrt(2+x) and g(x) = sqrt(2-x), we know that


f(x) + g(x) = sqrt(2+x) + sqrt(2-x)

Answer 7

that's what I got.. But, I wasn't sure if f(x) + g(x) = sqrt(2+x) + sqrt(2-x) was correct or not.. how would I find the domain?

Answer 8

yeah it seems too simple that it looks like a trick question, but it's not

Answer 9

the domain is the set of allowable inputs, or x values

Answer 10

remember that you can't take the square root of a negative number, so

2+x >= 0

and

2-x >= 0

Answer 11

those two inequalities become

x >= -2

and

x <= 2

which combine to

-2 <= x <= 2

Answer 12

so, in interval notation.. it would be (-inf,-2)U(2,inf) ?

Answer 13

no, [-2, 2]

Answer 14

that represents \(\Large -2 \le x \le 2\)

Answer 15

oh okay... and would this be correct? f(x) - g(x) = sqrt(2+x) - sqrt(2-x)

Answer 16

yes that's 100% correct

Answer 17

the domain is the same because the radicands (the stuff in the square roots) are the same

Answer 18

f(x) * g(x) = sqrt(2+x) * sqrt(2-x) ?

Answer 19

yes

Answer 20

domains are the same (for the same reason explained above)

Answer 21

domain is*

Answer 22

f(x)/g(x) = sqrt(2+x)/sqrt(2-x) and same domain?

Answer 23

the first part is correct, but the domain will be slightly different

Answer 24

now we have to avoid dividing by zero, so 2-x can't be zero

2-x = 0

x = 2

so if x = 2, then 2-x is zero. So we toss out x = 2 from the domain

So the domain is now [-2, 2)

Answer 25

so now what is the difference between f+g and fog(x)?

Answer 26

f+g means "add f and g"

fog(x) means "start with f(x), and plug in g(x) as the input"

Answer 27

fog(x) is the same as f(g(x))

Answer 28

\[\Large f(x) = \sqrt{2+x}\]

\[\Large f(g(x)) = \sqrt{2+g(x)}\]

\[\Large f(g(x)) = \sqrt{2+\sqrt{2-x}}\]

Answer 29

well it's with different numbers, I just wanted to know the difference.

Answer 30

i gotcha, do you see how I'm getting that?

Answer 31

f(g(x))=2+sqrt(2-x)?

Answer 32

f(x) = sqrt(2+x) and g(x) = sqrt(2-x) correct?

Answer 33

yes.

Answer 34

Then

\[\Large f(g(x)) = \sqrt{2+\sqrt{2-x}}\]

or

\[\Large f\circ g(x) = \sqrt{2+\sqrt{2-x}}\]

Answer 35

can you draw that? cause its not showing up correct.,. and im a lil confused