Question

f(x)= sqrt (x+2)
g(x)= sqrt (x-1)

find (f*g)(x)
(f/g)(x)

also find the domain of each

Answer 1

does the asterisk mean compostion?

Answer 2

like the first part is f(g)

Answer 3

you want
\[f\circ g(x)\]?

Answer 4

yes

Answer 5

not sure how you did the little circle

Answer 6

ok so it is
\[f \circ g(x) = f(g(x))=f(\sqrt{x-1})\]

Answer 7

=\[\sqrt{\sqrt{x-1}+2}\]

Answer 8

yes then you have to substitute f(x) in for the x

Answer 9

no you put g(x) where you see x in f(x)

Answer 10

do it step by step as i did and you will not mess this up

Answer 11

k i get the first part now :)

Answer 12

what about f/g

Answer 13

now you need domain yes?

Answer 14

\[\frac{f}{g}\] is trivial, just put f on top of g

Answer 15

k

Answer 16

hey satellite, can u come to chat if u don't mind

Answer 17

\[\frac{f}{g}(x)=\frac{f(x)}{g(x)}=\frac{\sqrt{x+2}}{\sqrt{x-1}}\]

Answer 18

now we do the domain. domain of f/g is x > 1 since the thing under the radical must be non - negative,and since it is in the denominator it cannot be 0 either. that is why you need the strict inequality.

Answer 19

harder is first one

Answer 20

@krish now that you mention it i do not see chat!