Question

I'm helping my nephew with a function question and i'm stuck on one part - I should know this really.

f(x) = x^2 - 19, domain = (-INF, 0)
g(x) = 1 -(1/2) x, domain = (6, INF).

Find range of f and g which i found to be
(-19, INF) and (-INF, -2).

Find fg - which I got to be (1 - (1/2)x)^2 - 19.

Write down the domain and range of fg.

- i'm a bit confused about this part.

Answer 1

I've done this stuff before but cant remember this bit.

Answer 2

hi. i think i can help. consider the intersection of the two domains

Answer 3

what is the intersection of the two domains?

Answer 4

well they dont intersect - which makes me think that the domain is that of g (6, INF)

Answer 5

the domain is the null set. and thus, it has not range either

Answer 6

it has no* range either

Answer 7

does that make sense to you?

Answer 8

hmm - not sure to be honest
- i'm not saying you're wrong - but i'll have to go back to the books
thanx for your comments

Answer 9

sure, the product, quotient and sums of two functions need to have intersecting domains

Answer 10

otherwise the function is not defined. I hope that helps. Take care.

Answer 11

ty

Answer 12

I've checked this out - because the domain of 'inner' function is (6.infinity) the composite function must have same domain - they intersect at that range of values
hers a rough (lol) drawing