Question

f(x)=1/√(x^2-4)
g(x)=√(x^2-9)
Find the domain of each of the following combinations:
f(x)+g(x)
f(x)/g(x)

Answer 1

I managed to find the domains for f(x) and g(x). Now where do i go from there?

Answer 2

take the most restrictive of f(x) and g(x)

Answer 3

wat did u get for domains of f(x) and g(x) ? :)

Answer 4

f(x)= x<−2,x>2 (−∞,−2) U (2,∞)
g(x)= x≤−3,x≥3 (−∞,−3]U[3,∞)

Answer 5

yes, so which one is more restrictive ?

Answer 6

domain of g(x) is more restrictive right ?
so domain for the combination wud be the domain of g(x)

Answer 7

yeah i though g(x) also. this means it applies to both correct?

Answer 8

also, for f(x)/g(x), g(x) =/= 0

Answer 9

it applies to both,
but for f(x)/g(x) u need add the constraint g(x) =/= 0

Answer 10

that gives domain of f(x)/g(x) as x < -3, x > 3

Answer 11

domain of f(x) + g(x) will be same as domain of g(x) : x <= -3, x >= 3

Answer 12

does that confuse u

Answer 13

this whole thing does but i think i got the hang of this problem

Answer 14

good :) in simple words :-
1) the domain of f(x) + g(x) must satisfy both f(x) and g(x)
2) the domain of f(x)/g(x) must satisfy both f(x) and g(x), AND g(x) \(\ne\) 0

Answer 15

Yeah. Thanks for breaking it down for me.

Answer 16

np :)