## cwrw238 3 years ago 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.

1. cwrw238

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

2. hsmt

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

3. hsmt

what is the intersection of the two domains?

4. cwrw238

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

5. hsmt

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

6. hsmt

it has no* range either

7. hsmt

does that make sense to you?

8. cwrw238

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

9. hsmt

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

10. hsmt

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

11. cwrw238

ty

12. cwrw238

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

13. cwrw238

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